You'd want the 280x for playing BF4, it's an AMD optimized game and mantle is on the way too, check these bf4 benchmarks (the OC 280x is on par with the 7970 GE/GHz Edition)
770 will run BF4 ultra no issue, but BF4 does favor AMD cards, and will be supporting mantle if you're into that. Here's some 770 BF4 gameplay http://www.youtube.com/watch?v=Tzs7tquJydI
The R9 280X may work a little better with BF4 being AMD optimized, but will Nvidias better drivers be able to counter act that? I feel like AMDs drivers are killing the game right now, and people with 770s are doing way better in performance.