for many years nvidia was market leader but with its latest batch of cards ati currently rules the roost.i cant give you a techy answer as im sure theres not a lot between them both but under official benchmark testing ati won out
If you have two nearly equally matched cards, for example the Geforce 5900/5950 and the Radeon 9800XT, then the stability of the drivers comes into play.
I have an Asus Radeon 9800XT/256Mb which was fine until I bought Doom3, where I experienced graphical corruption, apparently a known issue with the game and ATI based cards, but not with newer Geforce based cards.
Do as much research as possible before making a decision.
I think in terms of performance, provided you're comparing equal cards from both manufacturers, you'll see little difference in performance. However, I will choose GeForce over any ATI offering every time because experience has taught me that the NVidia drivers are always much better that ATI. Also, I run Linux quite a lot, and the NVidia Linux drivers are streets ahead of ATI. For me, ATI will always be the second choice to NVidia.