Which Is Better AMD Fx-8350 with ATi Radeon 7970 vs Intel Core i7 3930K with Nividia Ge Force 680

There is no point of going for GTX 680 at the moment.
The card is of older generation and GTX 770 is present now. It is just an overclocked GTX 680 and costs lesser too ($400).

GTX 770 is faster than HD 7970 by around 10%. I7 3930K Extreme Edition is the best processor you can find for $500 limit.

Definitely 2nd combination (GTX 770 instead) if you can afford that.