I have different sets of headphones for home and travel. I can't recommend any noise canceling in transit as I value situational awareness. I really love my Koss utility headphones. At home I still have big open-back cans so I can hear loud knocking or my family. I can't tell the difference between my old $100 Sennheisers and my $50 Samson SR850, bit I'm almost 50yo. I would look for whatever open-back cans have aftermarket earpads.

Former audio engineer here. Things that touch your body are highly subjective. Add in the audio angle, and the variables spiral out of control. Driver size is a guideline, but not an absolute litmus. This is a leaky comparison, but a great set of IEMs might have 10mm drivers. A high-end smaller driver will be more accurate than a cheap larger driver.

When I'm considering a new set of headphones or earbuds, I start by looking for aspects that generally outline a quality set of audio gear, such as AptX HD support, serviceability/rebuildable/parts availability, driver type and manufacturer, DAC manufacturer, wired option, etc. None of these by themselves are indicators of quality, but they are typically common to good gear. A published response curve from an independent lab is a nice-to-have. Once I approach the pull-the-trigger phase, I'll consider reviews from SoundGuys and people I trust in my circle.

ANC nukes audio quality. There are plenty of decent sounding cans with ANC, but they take an instant hit to sound and massive bump in price. In my experience, better ANC means lower sound quality. I prefer passive noise reduction for noisy environs. Comply foam eartips on your IEMs go a long way to improving isolation. Yes, this would mean a set of headphones and a set of IEM, and picking the right tool for the job. I've tried a bunch of ANC gear: Sony WF-1000XM4, Sony WH-1000XM4/5, Bose QC, Sennheiser HDB 630, and so on. In the end, I always go back to my wired hardware because it just sounds that much better.

Frequency response is the really the most meaningful tech spec. The larger the range, the more sounds the phones can reproduce on the low and high end. However, that does become less meaningful when listening to heavily compressed and processed sources. Also, I would guess that all the options you are considering have the same frequency response, so might not really be a consideration.

Bluetooth version is the next consideration. You want the newest version available, or at least no older than the version your source device runs. The higher versions provide more bandwidth, so theoretically less compression during transmission. It seems common to use older chips in more budget friendly headphones in order to save cost. The average user probably doesn't care, but if you are concerned about sound quality, it can be a factor.

Honestly, your source material is probably more of a hindrance to quality than your equipment. Compression is the enemy. Unless you are going to get into lossless codecs and/or analog sources, you won't be pushing the limits of the headphones you are considering. This is not to say you shouldn't get a nice pair, more just a fair warning that you're not gonna get a major quality boost from just changing your headphones.