One thing that hasn't been mentioned yet is interopability, that is, flatpak interacting with the rest of your system.
I'm not that familair with flatpak, but in my brief experience with the steam flatpak, I had trouble getting it to recognize my controllers. Steam installed through pacman (Arch's package manager) had no such issues, on the other hand. My hunch is that this has to with flatpaks being more isolated from the rest of your system.
Im pretty sure that's just some kind of permission issue, but it can be nice to not have to troubleshoot acces rights and the like. But this is obviously a double edged sword: more isolation may also mean more security, just at the cost of ease of interaction with other components.
Yeah, both have pros and cons. I have Steam installed through pacman and flatpak also. For me I have the Flatpak version because it contains its own version of glibc. This mostly doesn't matter, except I play Squad and it's doing something with it's anti-cheat that isn't supported in the most recent versions of glibc, so I use the Flatpak version for Squad only.
Flatpak is essentially a more controlled environment. It will contain everything it needs to work, which is good for ensuring it works but bad because you'll have duplicates. It mostly doesn't matter which you use, but occasionally it does.
This issue with glibc should have been sorted out. But yeah, if you use arch you may have some issues from time to time cause some projects broke their ABIs sometimes, but I prefer to use the one with pacman cause I only have to update my entire system with one command, also theming is an issue with flatpak that I know there is solutions out there but AFAIK are always adhoc solutions for each app.
Also, IIRC steam folder is always in a weird place using flatpak.