Have had different cards on and off for many years between the two, AMD/ATI for some reason does have better picture quality, noticed way back in the x800 days, I had a 6800GT and a buddy had an X800 and his games just looked better. Also had an 8800GT and the wife had a ATI 2900GT and her stuff just looked better, so not sure what image quality issues Nvidia is harping on about.
NVidia cards do seem to cope better with heavy AA. Not so convinced about the claim as a whole though. Game engines run different render paths depending on the hardware detected, so its pretty much impossible to test this on a level playing field. And if you push them all through the same render path then its not optimized correctly, which isn't fair either.