Whats your processor? Also you might want to check reviews for the stability of the card if its from HIS (make sure you keep your box). There are quite a few people that are bottlenecked by the cpu in crysis 3.
Depending on your processor, the 7970 might be pretty close to 680 and might perform better in single player due to physics being a bit intensive.
With one 7970 and everything maxed out and AMD optimisations turned off, I get about 50-60 average with an i7 980x@3.7ghz in multiplayer. Everything on low I get 120-130fps average in multiplayer with one card. On single player in the most intensive area on ultra with everything maxed out, except using SMAAx2 I get 40-50 fps average.
http://www.bit-tech.net/hardware/2013/03/15/crysis-3-performance-anolysis/5
However they were using older drivers and crysis 3 got a bit of a performance bump with the latest patch.