With Nvidia, runs straight out of the box as long as a newish version of WINE's installed, on ATI, not at all in my experience, at least on HD4870/4890. I had the latest proprietary ATI driver for Linux, driver enabled, direct rendering on, etc., etc. Immediate segfault.
I got the game to run one time somehow, flukily (never worked again), but even in the menu the performance was appalling, less than 1fps in the game. No luck with either of the open-source Radeon drivers either. Joystick worked fine (in fact, I've even used a PS3 controller to play SNES games on Linux). The only problem is, of course, TrackIR. But since I don't use one I wasn't that bothered.