Update: comparing the GTX760 to R9-270X
If we compare the same Asus cooler on both cards, the GTX760 averages 12% faster, based on 18 games so that's a reliable number.
Mantle in BF4 will boost the R9-270X ahead. Nobody knows yet, but I'd guess at a 20% difference, but then that would mean maybe only a 10% lead? Again, nobody knows yet; maybe will be really surprised... It's not just BF4 of course, but just how many games will actually support Mantle in the next two or three years will be small. By the time it succeeds (I think it will) you may want a new card anyway.
Just trying to be unbiased and provide ALL the info so you can make an informed decision.
NVIDIA BENEFITS:
1) NVidia Shadowplay (hardware recording of gameplay)
2) PhysX
3) G-Sync (requires new monitor in 2014 to work)
4) Gamestream (via Shield or upcoming device to HDTV from remote PC)
5) GTX760 averges 12% higher frame rates versus R9-270X (however VALUE is basically equal due to price difference)
6) Free games included with card.
There's no RIGHT answer for everybody. I hope you've found this pretty useful.
CARD LENGTH for Asus GTX760 DCU2:
8.6 inches !!
Power:
1x8-pin PCIe (or included 2x6-pin to 8-pin adapter)
Asus site:
https://www.asus.com/Graphics_Cards/GTX760DC2OC2GD5/#overview