7970 has better computing performance overall and is more future proof cause it is easy to reach high clock speeds by overclocking. But at that resolution you mentioned, both cards do very well in gaming. I would get a 7970 GHZ Edition. If you plan to overclock, a 7970 will be competing even a GTX680. At stock speeds though you would do fine with both cards.
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.
Yeah it's a hard choice but if you use a single 1080p with a 60hz refresh, as most are, and if you want physx it would be best to stick with a single 670 imo. If you use monitor with a resolution at 2560x1440, multiple monitors Eyefinity, then a 7970 may have some more value for you over a 670 otherwise it's a flip of a coin.
From a budget point, you are good to get hd7950 or gtx670 if you can afford. Bottom line: you can't go wrong buying any of these beasts, they will all satisfy you at 1080p resolution, almost any game and at higher resolutions they will all provide exceptional quality