The difference in video cards is between the developers, AMD and Nvidia. As for the boardmakers like Sapphire, Asus and so on, there is no difference, or only minor differences. The cooling solution of the cards is mostly what separates them. Some models might also give slightly better overclocking performance.
Titanfall
Playing at 1080p, a GTX760 will Probably be smooth at maxed out or almost maxed out settings. 70FPS average, with some dips. But the dips will probably not be very noticable. If you want to make sure to not see sub 60fps turn off AA.
If you play at 720p, the requirements for smooth gaming goes down. On the other hand playing with a larger 1080p monitor will be more enjoyable. But at 720p probably the GTX660 will be more than enough. You can play at 1080p with those cards, but with some settings turned down.
However turning quality setting down slightly in Titanfall, like for example texture quality, might not be very noticable. Yet might increase FPS somewhat.
http://www.gamersnexus.net/gg/1354-titanfall-texture-resolution-comparison
http://www.digitalstormonline.com/unlocked/titanfall-benchmarks-nvidia-gtx-780-ti-gtx-780-gtx-770-gtx-760-idnum168/
http://www.gamersnexus.net/gg/1352-titanfall-pc-gpu-benchmark-full-version
Note: Titanfall has just been released, and there aren't very many benchmarks available. Additionally since the game has just been released, perhaps both drivers from AMD, Nvidia and game optimization will increase performance.
If you want to make sure that you can max out quality settings, or you want to player at higher resolutions then consider the GTX 770 or GTX 780. The GTX 770 would be smoother than the GTX760. over 60fps with settings maxed, 1080p. Occassional FPS drops should probably not be noticable.
GTX 780(and above): super smooth.
If you will play at 720 or maybe at 1080p with some settings lowered then the GTX660 will be fine. If you will only play at 720p then you could probably even get a cheaper card.
don't take the above recommendation too seriously. I just looked at some benchmarks. And since Titanfall was just released there weren't that many of them.