i know you are probably sick of this question because many people have asked it, but i just wanted to know which one you prefer and why.
I would go with the GTX 770. Reason for this is the GTX 770 has a slight edlge over the AMD. Also, it uses less power and normally nvidia are better with their drivers.
I own both of them and they are very close to each other. Some games just work better with the 770 the same goes with the 280x. As far as drivers goes, never had any problem with any of them.
To me, it comes down to price AND if you have special needs that requires one or the other. The 770 does have a slight edge overall in my experience but the 280x is just a good value right now (in my location at least).
Both pretty equal. Comes down to specific games/applications, and price.
It would have to be the R9 280X for me, cheaper, just as good as the 770 in most games, extra 1gb of ram helpful for mods and certain games and simply because I don't like Nvidia.
That being said, GeForce experience is better than Raptr AMD Gaming Evolved if you like flashy overlays and software. The 770 is a really nice card, especially if you like Physx and other such Nvidia proprietary software.
I'd go with the 280X. It is cheaper and usually faster than the 770.
http://www.hwcompare.com/15840/geforce-gtx-770-vs-radeon-r9-280x/
read this for a comparison
Here is AnandTech's comparison of the two cards:
http://www.anandtech.com/bench/product/1041?vs=1037
Benchmarks of quite a few games at varying resolutions.