It really depends on what you're gonna play.
Some games are better optimized for Nvidia cards such as AC4 who has pared with Nvidia to bring out the best features to Nvidia cards.
While games like BF4 which will implement mantle to improve FPS.
Why not get the AMD equivelant of a GTX 780? a R9 280X? or R9 290?
TBH either way the card will do you fine, AMD cards have a slight edge on certain games and the same goes for Nvidia cards.
If you want my opinion I'd suggest get get the GTX 780 because of the free games. AMD's 'free games' are games from 2012 and even for the top end AMD cards you still get those 2012 games.
Its up to you though.
For the GTX 780 I'd suggest..
MSI N780 TF:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814127746
EVGA SC w/ ACX Cooler:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814130943
Gigabyte 3x Windforce GTX 780:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814125471
any of these three cards you won't be dissapointed with.
The evga has the highest clock, most expensive worst of the 3 at cooling.
The Gigabyte and MSI both have the same clock, roughly the same cooling with Gigabyte at a slight edge (awesome cooling btw).
The Gigabyte is very long so be cautious of that and find out its dimensions.
The MSI 780 is the cheapest of the three but has the best rating of the three on newegg. It's also the cheapest and a great overclocker.
Hope this can help you decide on what you want.
I'll try to include the amd equivelants but im at school right now and don't have the time to go digging about