I think it depends on the mobile device you use. I've read that proton is better on iPhone and bitwarden doesn't integrate that well with it but it's seamless on android. I also haven't had any issues with bitwarden and Firefox and they've been my combo since I started using bitwarden a couple years ago. I haven't given proton pass a full on try yet though and I pay both companies for their awesome services so I'm a bit of a shill for both. I don't think you can make a bad choice here.
I use Bitwarden on iOS and have for years now. I have never run into any major issues. Occasionally I’ll have to jump out to the Bitwarden app to copy a password but that’s usually because the website I’m trying to log into has their form set up weird/wrong.