The GTX 770 is a better card. I own a Gigabyte Windforce GTX 770 and it's fantastic, and it performs slightly better than a GTX 680. A GTX 680 is also a fantastic card, but the price of a GTX 770 is usually around $330 while a GTX 680, for whatever reason, is more expensive.
UPDATE: In fact, where are you finding these prices? The cheapest GTX 770 I can find is $330 while the cheapest GTX 680 I can find is $350. It's strange, since the GTX 770 is undoubtedly the better performer, but I suppose that's just one of these weird pricing phenomenons. Oh well, here's the cheapest GTX 770 I could find:
http://www.amazon.com/dp/B00CZ7Q028/?tag=pcpapi-20
And here's the cheapest GTX 680 I could find:
http://www.superbiiz.com/detail.php?name=ZT-680_2GP&c=CJ