Asus GTX 680 DCII 2 GB vs Zotac GTX 770 Amp 2 GB

Solution
Technically, 680 and 770 are the same card except that 770 is Overclocked. Whichever is priced lower amd take that one. You will be able to play all the games in ultra setting at 1080p you mentioned because it's a monster card.