Could FPS (frames per seconds) in browser-based games like Quake Live, Battlefield Heroes or Free Realms be affected by the browser version or browser type?
I mean choosing Chrome instead of Firefox, for example, could affect FPS or not?
Generally, no, not directly.
The game is executing "Out-of-Process", which means that the browser is not technically controlling the game, but rather sending commands to it.
However, The browser will consume memory, and possibly CPU cycles which could have a negative impact. This will, of course, be the same as having the browser open at any other time.