HD 7770 seems to be a little faster than the GTX 650, but the Nvidia card has got 2GB GDDR5. Also Nvidia supports PhysX, has a better 3D vision, has got better drivers and they are updated very often.
I hate AMD cards because I owned a few of them and ALL of them gave me problems (9600PRO AGP, HD 3450 AGP, X1650SE, HD 5670, HD 4870x2).
If you can, go for a GTX 650 Ti... If you can't, go for the GTX 650... Also 2GB of GDDR5 memory are really better than 1GB, especially if you use high resolutions and high settings in games. 1GB are not enough to run some games decently...