Go for the R9 280X it performs better than the GTX 670. Don't even know why the GTX 670 is at that price the GTX 770 is only a bit more than it. As an added bonus i think you get free games with the AMD card too.
280x barely edges it out. And it is newer than the 670. I guess the 280x has more VRAM?
Yes, but VRAM doesn't improve frame rate. Just enables more AA, DOF, textures, etc in-game. And if you look at the link I posted above, you'll see that the 280X does a bit more than just 'edge' it out.
Funny enough, the R9 280X actually still edges out the GTX 770 in some games. (Unless its a game that utilizes nvidia voodoo and intentionally screws over AMD cards, see: watch_doges)
Grab the 280x put the money you were going to spend on the 770 towards something else you could possibly upgrade eventually like more memory or an SSD.