That comes down to preference and games you play, as well as resolutions.
First off, strike the 4GB version of the 770. In most cases, it's a waste. The 2 GB version is fine. If you are playing at 1080p, the 770 pulls ahead of the 280x more often than not, but not by a whole lot. If you're gaming at 1440p, the 280x starts pulling ahead due to the extra VRAM (not a factor at 1080p) and wider memory bus.
So assuming you are at 1080p, it really is down to preference. The 280x will feature Mantle, while the 770 has physx, shadowplay, and a few neat tricks like TXAA (low cost AA). Again, the 770 is a little stronger at 1080p gaming, but the gap is small enough that it's not that big a deal. You'll be happy with either one.