It was a tough one for me as well bro.
You need to make a list here and decide which one you ultimately want. Like:
1) R9 280x has 1 GB more VRAM, will be useful for you? You can 1080p monitor and in some games it can easily use up 2GB. Question here is, is 1GB really needed? Answer imo is no but it can be handy in some games like skyrim, hitman 5 etc.
2) GTX 770 seems to give 5-10 fps more than R9 280x in some scenarios while R9 can also beat 770 in some games. Overall upper hand is of 770 while in compute related tasks r9 can't be beaten by 770 by a long shot. Gamers don't care for it though.
3) 770 has CUDA and Physx which some games like Mafia 2, Batman (?) etc use. AMD has mantle which BF4 and some future releases are going to use.
4) 770 uses shadowplay with the help of CUDA. While AMD R9 has App acceleration for the same thing but requires a software like Bandicam for game recording.
5) I personally always liked Nvidia's driver support and graphics interface\panel for every other game. AMD's CCC\catalyst is not appealing or helpful imo and i never liked it much, though one can use a free software like Radeon pro to compensate here.
Btw which version of 770 you're looking at here?