Now that you know what Resolution you'll be playing at, now you can make your decision, based on your budget, on which video card to get.
The Radeon 7770 is OK at 1080 but the 7870 is MUCH better. It also boils down to what games you'll playing. If you want to play the latest and greatest, then go for the 7870. If you stick to older MMO's / FPS and you don't mind not having all the eye candy turned on then the 7770 is a great buy for around $100. You're going to pay double for a 7870.