The 6850 is quicker. No argument. But not by a huge amount, and the 7770 is much more energy efficient. So it depends whether better energy efficiency is more important than a few more fps.
As stated by SteveH3671, the Radeon HD 6850 is overall a little faster, but it also consumes more power. Below are summary charts backing up that claim from Techpowerup. Note that the overclocked Sapphire HD 7770 Vapor-X does match the performance of the Radon HD 6850.