I believe the 8800 ultra would be slightly faster than the 7770 but visually in more recent games I believe the 7770 would be a much better choice as it will be will have significantly better power consumption and better performance under high level AA and anisotropic filtering compared to the 8800 plus the 8800 is very old so its DX support is greatly outdated in new games in which 7770 supports DX 11 I believe. So if you are using for current gen gaming I would recommend going for the 7770.
The 7770 will have much better support for current games than the 8800 ultra. The 7770 is newer and supports DirectX11, which modern games run on which the 8800 ultra dosen't have. Overall, i think the 7770 is better.