Apparently ATI has better AF while NVidia has slightly better AA, although I have personally used Adaptive AA with several games and it looks very good. Also, the X1800XT can do FP16HDR + AA(it;s usefulness is debatable however), which you can't with the NVidia card.
As for performance they are about equal with the X1800XT usually winning in DirectX games and the 7900GT winning OpenGL titles, and the X1800XT takes a smaller performance hit when you enable AA and AF. Also, you can voltmod and overclock the X1800XT within software while the 7900GT will require a hardmod to up the voltage but can clock very well if done.
Think about which games you play, look at several reviews that compare the two, and then buy which one suits you. You can also search these forums as there were several 7900GT vs. X1800XT threads.