Based on our tests, it's pretty clear that the GTX 560 has a raw performance edge over the competition from AMD overall. However, that performance advantage isn't huge, and the Asus Radeon HD 6870 TOP has the distinction of being uncannily quiet for a $200 graphics card. Oh, sure, it draws a little more power at idle, but that doesn't seem to affect noise levels.
In the other corner, the GeForce GTX 560 TOP is faster, nearly as quiet, and costs only $20 more. It has company, too. MSI's GeForce GTX 560 Frozr II is almost as quick, only a little bit louder, and $10 cheaper. While neither card has hexa-display support, both let you enjoy Nvidia-specific perks like PhysX and GeForce 3D Vision. Some users like those extras, while others couldn't care less. You can make up your own mind on that front.