Since wine is mostly developed and tested on nvidia cards, it works better there. That's partly the fault of fglrx-bugs and partly the fault of wine devs not caring.
But don't worry, switching to nvidia will just replace your current problems with new, completely different ones. I've switched from a GT7600 to HD5770, had some problems go away, other problems appear. The two major arguments for nvidia are VDPAU and wine, if you care about these (and don't care about OSS support or eyefinity), you may consider switching.
Be advised though that even with nvidia, not every wine game will work flawlessly (in fact, most don't), and sometimes dual-booting is the cheaper and easier solution.