1) The 7970 GHz is better because it is just flat out stronger than the GTX 680, and always has been.
Overall the 7970 GHz is ~5-10% stronger than the 680 since the 12.11 driver update as shown here:
http://www.techpowerup.com/reviews/AMD/Catalyst_12.11_Performance/23.html
2) In addition to this the 7970 GHz overclocks far more than the 680 does, and when this is taken into account the lead increases in AMD's favor. (Don't be afraid of overclocking btw, its super easy and safe as long as you aren't insane).
3) As for "The way it is meant to be played," Metro: 2033 is a Nvidia meant to be played game and yet the 7970 GHz stomps the 680 by a resounding 26% in 1080p as seen here:
http://www.techpowerup.com/reviews/AMD/Catalyst_12.11_Performance/13.html
As you can see "The way it is meant to played" means nothing and is just a marketing gimic. Usually it just means Physx was tacked on with the sole exception of Borderlands 2. However I have BL2 and a Radeon card. My PC can still handle physx fine on high, and easily on medium, but I just don't think it is worth it. Even when I had Nvidia cards, I never used Physx. The performance hit is almost never worth it.
4) However the 7970 GHz uses a bit more power than the 680, which I know can be costly in europe. However I still don't think it would be enough of a difference to matter, and if you want to save power get a GTX 670. The GTX 670 uses less power and is roughly the same as a 680.
Hope I helped!