In my opinion the Nvidia 770 is way better than the AMD R9 280X. If you wanted to compare the 280X to a Nvidia card. Then it will be between a Nvidia 760 and 770, which there isn't a card like that. So what I am also trying to say is the AMD R9 280X is still a great card.
So between the two, you may already know that the Nvidia 770 is way better in performance. So what else is so special about this and what we may need to consider?
Nvidia consume less power than AMD and you can take the advantage to record gameplay with Shadowplay, but Mantle still isn't that well know yet.
You will need to take the PSU into consideration if you do get a AMD R9 280X, a 550W is preferable. Please tell me your PSU.
And one ire thing both cards will go well with FX-8350.