If you are looking at specifically the 7970 vs the 770, not the 7970ghz then I do believe that the 770 is superior. I'm also pretty sure that Nvidia cards run quieter and cooler with less power consumption than AMD, but i could be mistaken.
If you are asking about the 7970ghz vs the 770 then they are approximately tied but depending on the game the winning card will fluctuate. The 770 would come with PhysX, which makes sexy particle effects in games, and GPU Boost 2.0 for some mean overclocking capabilities. The 7970 itself does overclock really well and can probably reach the 770's base levels when overclocked.
The 7970 does come with 3 (or 4, idk if Tomb Raider is still included) games which is always awesome
You can either play them or sell them or whatever you want.