I cannot choose between the two. The AMD Radeon R7 265 delivers more FPS, but the Nvidia GeForce GTX 750 Ti draws less power. I will be playing Battlefield 4, hopefully at 60 FPS, on a 1920 x 1080 resolution monitor. What would you pick, and why?
If running a second card is a future possibility, the GTX750Ti is off the table. Otherwise, that's probably the one I'd pick. I believe there is a good bit of variability in the benchmarks, and I personally like to keep power use down (make sure your PSU is enough for the card you choose; a 300W PSU will run the GTX, but the R7 should probably have 380W+). I fully understand that those not concerned about power will disagree with me.
That's too much to pay for either of those cards. The r7 265 (HD 7850) is often on sale for $100, and I have seen the GTX 750 Ti go for $130. For $170 I would be looking at a slightly used 280x. There are a ton of them in various tech forum marketplaces.
But, between the two models mentioned, I'd get the r7 265 over the GTX 750 Ti unless your power supply is weak.
i would get the 750 ti, in my personal experiene in bf4 my 7770 and r9 290 had stuttering issues, while my 780 and 580's did not, also it uses less power which means it will run cooler n quiter, some people may not worry about this but the less noise your pc makes the more you will be immersed in your game.
sidenote, gcn cards still have terrible performance in dx9 games, so if you plan on playing some other gams this could be an issue.(especially WoT, a game i highly recommend )