I use Firefox on both Android and desktop. It's much better in many ways, and I love it. I do get compatibility issues sometimes, but I'm unsure whether it's because of all of the add-ons I use, or websites being buggy with Firefox.
Caveats: Sometimes launching apps from the browser only works in Chrome and some demos of bleeding edge experimental Chrome features obviously don't work in Firefox.
Mailgun is one of the worst offenders. when I mentioned to their support that auth among other things was broken in Firefox, their response was "use chrome"