Which graphics cards are better: nVidia GeForce or AMD Radeon?

Its really a matter of personal choice. ATI tends to have cheaper cards that give you better bang for the buck (at least from my viewpoint) while nVidia cards tend to cost more, but have higher total output.
Also, some games are designed to run on one card, so the opposing card, while still able to run the game, will not do so as well.