7850 is much, much better. If you want to play BF3 get 7850, no doubt about that. It also has very nice overclocking potential. I suggest you get the Sapphire dual fan version which is uber quiet.
The 7850 is faster than a 7770.If your looking to max it out and get a 60fps average your going to need a 7950.But the 2GB model either way is a must if you want Ultra.