ATI has some cool AA that works on every game using a 3dfx system
On the other side, nVidia has physx (that is far better than Havok by ATI).
FXAA and TXAA by nVidia if i remmber right must be implemented in the game itself fot it to work.
On the other hand, the 7970 is better, but will run very hot, so i STRONGLY suggest you at least change the thermal paste and if possibl use a custom cooler for that GPU.
Since you have a strong CPU (physx should not be a problem if runned by the CPU), id advice ATI over nVidia at this point.
However, if all you look for is raw performance power, both are great options and as some have mentioned, you wont go wrong either way.
EDIT: Also note that while full hd is great on a 24 inch monitor looks great, with no AA on a 46 inch TV... it might look jaggy.