It's not the answer you want, but Wine needs _a lot_ of features from the graphics drivers that ATI simply does not provide. In addition, some recent D3D work regressed on ATI drivers, complicating things a bit more. Nvidia has been better about providing good drivers, unlike ATI. Most native games don't require as many resources and hence, work fine. You might try disabling compiz if you haven't already, as it conflicts with wine. Also, try filing a bug with ATI. They won't fix bugs exposed by wine's graphics tests, but will fix bugs affecting games...
