I think the GTX770 is a better card.
If you compare the OC'd models the 770 actually is faster on average such as the new MSI GTX280X vs the MSI GTX770 TF. The VRAM isn't a big deal even in BF4 if you properly analyze the results. 2GB is still fine.
Not enough to really matter so it comes down to other things, and there are some important differences:
1) Games package. The 770 has:
- Batman Arkham Origins
- Splintercell Blacklist
- AC4
That's $150 in new games. What does the AMD have? Seriously, I couldn't find that.
2) G-Sync:
This is so new you may not have heard of it but it's a big buzz and the top guys are really excited. You do need a new monitor which supports it but it solves the biggest game headaches:
-lag
-stutter
-screen tearing.
I'll leave it to you to research, but I saw videos of John Carmack and Tim Sweeney discussing it. It's really sweet (though ironically I'll buy a new monitor and NOT upgrade my graphics card now).
3) PHYSX
4) SHADOWPLAY
Allows recording/streaming at 1080p @60Hz with little to no frame rate drop. (I tested it in Skyrim with VSYNC OFF and my frame rate stayed at exactly 78FPS)
Summary:
I'm just throwing this info out there. I was recommending some AMD cards a while ago when they had great game deals, now I'm recommending the GTX770.