Important for what? Are oranges better than pumpkins?

For me it is definitely perception. There is a German saying which goes:

Gut gemeint ist nicht gut gemacht.

Which literally translates to „well intended is not well done“ and I agree

Honestly, intent. The issue is that another person's intent can't ever truly be known. All you have is your perception of their intent.

But I weigh my perception of someone's intent more than I weigh their outcomes

I think intention is more important, but perception of your intentions can have just as drastic consequences.

And of course just because you have good intentions doesn't mean you're doing the right thing.

The question is flawed.

When dealing with others, there is only perception. Even if I really try to understand their intention and they really try to communicate their intention, all I will ever have is my perception based on my understanding of what they tried to convey.

Only you know what your true intention is, perception is how the world sees you.

Sounds like we're talking about a speech act.

If the question is intention vs. perception, intention all the way. Perception of a speech act should track the intent of the speaker, otherwise the perception has failed.

There are of course ways a person can make their intention clearer, particularly by following rules/norms of communication, and a person receiving or processing that communication should also utilize understanding of those rules to interpret (to properly perceive) the information.

But if both parties are doing their level best to clearly encode and decode the information, but the perceived message varies from the intended one, which one is closer to the truth? Intention. And over the long term truth wins out.

Perception is subjective, intention less so, intention takes priority for me

They are both equally important. However, we tend to judge ourselves by our intentions and others by their behavior. Considering this, I think it's important to continually try and understand the intentions of others, and consider how our actions might be interpreted by others.

Perception. Everyone knows what they think they heard you say. Very few people are privy to why you said it. The perception of what you did has a far greater reach than the intention, and is therefore the more important thing to control. This was as true in antiquity history as it is today -- although the Internet certainly amplifies this effect.

Did Nero really fiddle while Rome burned? Did Marie Antoinette really say "Let them eat cake"? All that matters is public perception.

Machiavelli covers a lot of things like this very well, I feel he's unfairly maligned -- most of The Prince is ethically-neutral and practical leadership advice.

Perception.

All we can go on really is how we perceive others actions (or what they say) and the intent that we can gather from what they do (or say).

And all of this runs through our filters of past experience and what we've perceived others intents to be in relation to the things they've done (or said).

For example: I'm really quick to pick up on people using emotionally abusive/manipulative language or acting in abusive/manipulative ways, this is because I've (unfortunately) had so much experience with abusive/manipulative people. I've spotted it incredibly early in relationships, not only my own but the relationships of others. People don't like getting called out on it, and people really don't like it getting called out when they don't see it in their friends or partners.

"They're not like that with me."

"They're only like this sometimes."

"Well I did kinda deserve it."

I call it out when I see it, because abusive and manipulative behavior left unchecked will only fester.

Better if you can achieve consistency in both.

What’s your context? Is this a theological question? A legal question? A political question?

Intention tells everything about you and perception tells basically nothing

Maybe ask Paul Watzlawick. Or since he died in 2007, you can read one of his very entertaining books.

I know this is a few days old, but thinking about it again, I'm reminded of this clip I saw from Orange is the New Black. To summarize, the clip is a flashback to explain how Suzanne ("Crazy Eyes") wound up in prison. She's an autistic woman whose sister/caretaker leaves her alone for a weekend, without arranging alternative care, to go on a vacation. She befriends a child, who she seems to connect with easily as they are on a similar mental level, and the kid follows her home to hang out and play video games. After the child says it's time for him to go home, she becomes upset, blocking the front door to prevent him leaving. He attempts to call 911 and she grabs the phone and hangs up, confused, telling him that he should only call 911 for emergencies. Panicked, the child attempts to crawl out a window to escape, accidentally falling to his death.

What would you say is more important here, intention or perception? I think it depends on who you are. For the child's parents, perception matters more. Their child is dead. That Suzanne didn't intend for it to happen is of little consolation. For Suzanne, maybe intention matters the most. For the courts, both matter; she's proven herself unsafe to be around to the public, yet the fact she didn't intend to cause harm is supposed to be taken into account too, perhaps for lighter sentencing. In a better world, she would be given help instead of incarcerated because of her intention, and perhaps her caretaker would be held partially responsible.