I just bought a EVGA GTX 680 SC. I tried to run Crysis 3 max settings and I was lagging pretty bad. Not sure the exact fps but below 30.
It might be that the processor/ram or something is bottlenecking my system.
Use FXAA if you aren't already.
The difference certainly isn't worth the price, a decent 670 should overclock higher than a 680. Thats not to say a 680 doesn't overclock, but the difference is certainly minimal. If you consider the price difference between a top end 670 and a reference 680 the 670 is a far better buy, considering noise and heat the OC headroom is far greater.