Considering only those two cards in your wishlist, then I would choose GTX 770 engine if there is no financial constraint yet r9 280x is still worth a lot. There are numerous online benchmarks, comparing both of these cards. Though GTX 770 has bagged the place, its real time performance is negligible with 280X's. Believe it or not, it is true. The price difference between these cards is around 90$ (Approximately) but the performance difference is just around 8%.
It's like you're paying 90$ more for nvidia just to obtain 8% performance higher than AMD's. Let me show you few benchmarks.
> AnandTech:
http://www.anandtech.com/bench/product/1041?vs=1037
> TrustedReviews:
http://www.trustedreviews.com/opinions/amd-radeon-r9-280x-vs-nvidia-geforce-gtx-770-which-is-fastest
> Pcadvisor: http://www.pcadvisor.co.uk/reviews/pc-components/3504251/amd-radeon-r9-280x-vs-nvidia-geforce-gtx-770-comparison-review/
Not only by these but I've tried those cards in real as well. If I'm at your place, I would go with R9 280X with no hesitations because IT IS THE BANG FOR THE BUCK. Specs-wise, GTX 770 may look better like 70% higher but when it comes to gaming in real time, it has just proved to be an very expensive card and you can even buy R9 290 in the similar price which is far better than 770. 290's texel rate, pixel rate and clocks are really commendable and worth buying. So choose your card wisely, OP. And hey, r9 280x is also a good overclocker. I use R9 270X of MSI's and I have superclocked it.
Edit: I must admit that I've quoted a much pricing difference. My apologies for the inconvenience. It seems only 20-30$ difference. Credits to i7Baby and Proofy.