Please read 
I enjoy both but its really cemented why I love dragon age so much more.
These are story based games set in worlds created entirely for these games. Its common to have discussion about how different story events could have gone differently, or what will happen in universe after the events of the most recent installment. Obviously, how these worlds are set up and how the story is told effects the discussions a lot.
In mass effect society spreads across the galaxy and encompasses trillions of individuals across thousands of planets. Despite that, the major story beats hinge on how you treated individual characters, or whether they are alive or not. Like whether an artificial plague causing 99% of krogan pregnancies to miscarry is justified is completely down to whether the good leader is in charge.
Despite trillions of individuals and complex economics all major conflict boils down to species versus species. All krogan, all asari, all turians are just like that so of course this has happened. There are hints in game that there are many different cultures within each species but we get very little evidence of that, and almost entirely in the 3rd game. Krogan (giant toad people with natural armor, anger issues, and a love of violence) are shown to be maybe not inherently violent individuals that care a bit about others, but thats mostly it. We get one pretty butch Asari (otherwise all feminine species).
So when the community talks about these things its always on individualist or species based terms. It is almost impossible to do materialist analysis because of how the games are made. When the community talks about the game arguments are more heated and personal. There are lots more gotcha type lines than in the dragon age community. I suspect this hostile dynamic could contribute to why there are obviously way more women and queer people in the dragon age community.
Mass effect's story is also about exceptional individuals overcoming impossible odds, which lands way better with men, in general, than women, in general.
In the dragon age community discussions revolve around things like, how does the church use drugs to control their private army? How will giving the dwarves a tool that enables them to put their souls into tanks effect their society? How do independent kingdoms respond to a paramilitary organization run by a prophet encroaching on their land?
Mass effect discussions are, "do the volus deserve a council seat?" Instead of, "How could the Volus get a council seat?" or, "How will the volus having a council seat change existing power dynamics?"
Dragon age stories are, "how does magical talent being both random and dangerous effect society?" "Is it worth it to consort with demons to gain power?" Mass effect stories are, "oo ouch owie my magic gives me migraines." (I like Kaiden don't @ me, the whole child soldier bit both games have is nice)
There are other differences too, like dragon age having braver character writing that scares away some of the chuds. Most people on the dragon age subreddit don't like Vivienne, but understand how her inclusion makes the game better. That kind of subelty doesn't exist in mass effect discussions because the game literally wasn't designed for that level of depth. All characters that are apart of your "squad" are meant to be likeable or at least the kind of person their players would respect. Dragon age release characters also in your "squad" like Sera and Vivienne knowing that tons of their players will hate them.
In summary, mass effect is lacking a pair, let alone a quad. (krogan have 4 testicles) (Please laugh I mentioned testicles)
This is underselling ME3 a bit, it was relatively anti-gamer for its time. ME1 and 2 get the 
tho. Even though I like them anyway.
Edit: how could I forget Dragon age has literally actually good trans representation. Theres a FtM guy whos literally just the coolest fighty bro and his dudes respect him.
"So If I grew up under the Qun they'd treat me like a real man?" "You ARE a real man Krem." 
Edit 2: adding data from reddit surveys
The dragon age subreddit is 45.2% women (3.2% trans), 44% men (1.9% trans), 9.1% non binary and 1.7% other. 45.3% Heterosexual
The Mass effect subreddit is 76.4% men (0.6% trans), 19.7% women (1.5% trans), and 6% total trans people. 73.9% hetero
Dragon age reddit 2023 demographics survey: https://docs.google.com/forms/d/1vi-9XTyIx2kvu4hXb309b0NvdWL7Ub_Yj73le6WXzpI/viewanalytics
Mass effect reddit 2019 demographics survey: https://docs.google.com/forms/d/e/1FAIpQLSdNHQxT7COKRuYIaoHBXt0s3DOdq2RgPCLlJg2RCN5pf3kcKA/viewanalytics
Counterpoint: literally everybody hates James. Seriously though, I think this is just due to Inquisition being a more recent game than ME3; IIRC chuds also hate a lot of the Andromeda characters for being POC or LGBT. I'll definitely concede that IIRC there are no trans characters in ME which is kind of odd. As for the gender distribution between the two franchises, toxicity is definitely a major factor, but I wonder how much also has to do how the franchises were structured. ME was a complete series that started in '07, which was prime Gamer^tm^ time, and jumping in at 2 or 3 wouldn't make much sense. DA started in '09, but the next two games were totally unrelated meaning people could jump in wherever, and over time it has become more socially acceptable for women to play "real games". In both franchises you more or less play unaccountable secret agents working with a ragtag team of weirdos to commit mass murder, so it's not like the tone is that different. Maybe also something about genre, with fewer women wanting to play a TPS?
I disagree that DA is more about societal problems rather than individual ones. Maybe it's just because I played Origins the most (2 was okay, Inquisition was garbage), but I remember having to choose between "good and evil leader" in the dwarf quests or "evil elves and good werewolves" in the elf quests, for instance. Both games have the same core problem: they're made by liberals and so usually have one obviously better solution (though occasionally there will be a secret third option, typically based on compromise, that was actually the best choice all along!). I think the biggest difference is the paragon/renegade system: there was never a time where just doing the paragon thing wasn't the best option, and that drastically limits how they can write stories. Whereas the dwarf quest has "the nice traditionalist and the asshole reformer", and you can make arguments for both sides, Mass Effect has "cure the genophage or don't because lol lmao".
Anyway, the most important thing here is clearly ranking the different games were: ME1>DA:O>>ME2>DA2>>>DA:I>>>>>>>>>>>>>ME3
This is official and definitely has nothing to do with nostalgia.
counterpoint: they don't get props for making a black man with an absent father cheat on you. And they clearly tried to make him a likeable character but then just made his romance shitty. He's just boring. Oh! James not jacob. He's boring too and he wouldn't stop flirting with my shepard. He's meant to be shepard's bro guy, they still tried, even if they failed.
Shepard is "the best humanity has to offer." The Warden is the new guy who lived because they were given the boring job. Hawke is a poor refugee who gets caught in some big trouble. The inquisitor got their power completely on accident. Both are individual stories as a consequence of the agency bioware games give their players over the plot. But everyone is literally slobbering on shepards toes the whole trilogy, especially 2 and 3. You get more of that than I'd like in DA, but its way less than ME. Shepard also has big cop energy that DA doesn't.
My point wasn't that there aren't good guys or bad guys. Or that the choices were complex and difficult. Just that what defines your decisions in dragon age games are the systems that individuals are a part of, not the individuals. Curing the genophage good if wrex and eve alive, bad if wreav and no eve. No societal pressures, no politics, economics, just chad wrex putting his species on his back. Though tbf they make it clear eve will end up being more in charge than wrex. They actually cut a pretty matriarchal line with the krogan that I liked.
If you restore the anvil of the void in DA its bad no matter what. Because the power incentivizes unethical behavior.
Yes, the brecilian forest is the weakest part of DAO.
Also, there aren't any compromise koombaya decisions in Dragon Age. At least not that are clearly the best decision. The closest you get is getting briala and celene to marry and rule together in DAI, and getting alistair to marry anora. I chose neither in my cannon playthrough. There are a lot of, "solve the underlying issue if you did things in the right order," though.
I think if you're looking for a big picture non-writing team reason for the difference its that DA games have different protagonists. Everything relates back to your decisions over the trilogy which forces it to be very individualist.
For me its inquisition (with DLC) > DAO > DA2 > ME1 = ME2 > inquisition (base game) = ME3.
Might give Inquisition a go, I was so put off with how much they changed from DA:O I never bothered with the sequels.
This is not my first time proselytizing. Check out these comments from a year ago to get the most out of the game.
https://hexbear.net/comment/3431009
Lol I played DAI at launch so I guess our opinions match. Surprised the DLC could make that much of a difference, honestly.
The Descent is the best dungeon in inquisition. Jaws of Hakkon is the best open world in inquisition. And Trespasser is my favorite RPG experience of all time.
I think the main difference between DA and ME is based on the people that made it. I was in the forums an embarrassing amount from a couple of years before it released until somewhere after DA2.
The writers were actually able to write “romances” that would appeal to women, mostly due to the team being a gay lead writer, 4 women and a straight guy. This also carries out in the fandom, the most noisy people after release until I stopped going were by far horny army wives. There was always a much more even gender distribution in the DA forums than ME, so I don’t think it is Zeitgeist.
1
Hainly Abrams in Prodromos, Eos in ME:A, she's pretty poorly written, not necessarily in a transphobic way, the convo is just strange and clearly written by a cis person (and then dev crunch being too big to give it a second thought). They reordered her dialogue around so it's less strange now, but it's also made it more difficult to find out she's trans (which, tbf, isn't necessarily unrealistic)
i'm afraid we must split the left
What order would you put them in?
sth like
DA2 > DA:O = ME3 = ME1 > ME:A >>> ME2 >>> DA:I
ME2 is so frustrating to me the way the main plot and Shepard are written
Inquisition I can really see why people like it, I just... don't
I'm super curious about your frustrations with ME2. I don't think I've ever seen anyone rank them 3 = 1 > > > 2. Its almost always 1 > 2 > 3, 2 > 1 > 3, or 1 = 2 > 3
And yeah. Inquisition was my least favorite dragon age game until I replayed it with mods and the DLC. The DLC is the best part of the game for me. The main quest is easily the weakest of the 3 games. Plus the ubisoft open world bloat was a bummer. If you approach it in the right way, with the right mods, it makes the game a completely different experience than what most people had their first time.
Main thing for me is that Cerberus (and Shepard's relationship to them) in ME2 is terribly written, and it's bad in a way that it really gets in the way of me enjoying the game. Like, a lot of the actual bad stuff Cerberus has done in ME1 as well as Ascension gets ignored for the sake of having Shepard work for the 'morally ambigious/grey' organisation. Which gets extremely frustrating when, unlike the game, you do remember what they did.
There's this really funny moment when you take the shuttle off of Lazarus and Jacob and Miranda do a little interview, one of the things they ask about is your psych profile. Cue Jacob asking a Sole Survivor Shepard if they remember the thresher maw attack on Akuze followed by a deafening silence as you're sitting there "Hey, wasn't that you guys who did that?", Shepard says nothing of substance and it never gets brought up again. There's this clear conflict there that the game seems so uninterested in exploring, you never get to materially do anything about it. At most Shepard gets to throw a tantrum and flail around a little bit before swiftly being put down by TIM or Miranda.
And like, ME2 has a lot to like, there's a reason it got like a 95/100. Cause like, all the recruitment and loyalty missions? Fucking incredible. It's just tainted by this main plot that really ruins my enjoyment of it
As for Inquisition, I've heard the DLC is definitely better, I've just never managed to slog my way through the main game to get there 😬 One of my main issues is just that the Inquisitor is really dull and disconnected from the world? And it really drags down the rest of the game with it for me. (also as an avid chantry explosion enjoyer the way they did the mage - templar war dirty makes me so mad lol)
The decision to make you work with cerberus was always strange. I think its a symptom of the game only having factions representing, the council. the species central governments, mercenaries/organized crime, and terrorists. But, they gave you a ship and a lot of autonomy. If you accept the in game premise that cerberus is the only faction willing to act against the collectors it becomes easier. But working with cerberus will always feel off. It is nice though if you have Miranda in your party when you blow up the collector base she quits cerberus. Really pisses off TIM.
I didn't finish inquisition on my first playthrough either. It was only after coming back to it that I learned to appreciate it. Now its one of my favorite games ever. I have a post here where I talk about how to get the most out of inqiusition. Depending on your choices in game you can have a pretty satisfying conclusion to the mage rebellion at the end. How would you have done the mage - templar war differently?
I should clarify that it's not that I've played Inquisition once and didn't like it, I've played it like a dozen times with ~250 hours in it, thinking each time that I'll actually like it this time, so I've kinda grown weary of the idea that I actually could at this point haha
For the mage - templar war, like, anything would have been better. It's borderline set dressing the way Inquisition did it. There's barely any context given to what has actually transpired since DA2, and the actual warring factions are just reskinned skyrim bandits in a few places in the Hinterlands. They're just there, they're hostile and you kill them, you don't get to talk to them, or know why they're actually out here fighting. You just wordlessly wipe them out and go talk with the Reasonable Moderates™. Then the entire plotline over just as soon as the game has started, no like ultimate conclusion or victory, no promise of a better future, no rebuilding, just "the Inquisition needed bodies, so we threw a coin and picked a side"
Yeah thats fair. Sorry you've been duped by the game like that. A couple of games have done the same thing to me, fallout 4 being the most prominent example. It sounds like you never got to play trespasser, which would be a huge shame (to me).
I super agree. Most of the actual ground work of the rebellion was laid in supplementary books (that I haven't read). They really should've restructured the plot so that ending the mage rebellion and recruiting your chosen faction would've been the first two acts, instead of only the first act. The plot went in a lot of different directions, which made it unfocused.
I challenge the idea that you work with the reasonable moderates though. Fiona worked for years to make the rebellion happen. The reasonable moderates are people like Vivienne, Wynne, Cassandra. Fiona started a violent revolution to free her people. The ones who you fight are essentially cells that went rogue.
in case you never actually finished inquisition spoiler
you can make leliana the new pope. She legitimizes the free mages in the eyes of the chantry and lets them form their own independent college. She also lets all men and all races take the chantry vows. Previously it was only human women. She also purges super aggressively in most endings lmao. We will make the chantry sunshine and rainbows and I will murder you to make that happen >:(