The 660Ti will more or less be more faster in games, since most of them are more optimized towards nVidia users.
I don't exactly remember which latest DX 11.x it supports but microsoft is promising DX12 that will work with previous Fermi and Kepler cards. So that's something to look forward to.
Looking at all sorts of benchmarks, I believe that the 660Ti will have better average fps and won't have as much lag spikes, should you use higher resolution in-game or Hi-Res textures.
Just make sure the card has at least 2GB of memory since it should be standard for entry/mid level gamers nowadays.
Pick either ASUS or MSI flavor both are good, unless you don't have the option. In my honest opinion the Twin Frozr beats Direct CU II slightly.
If you could get a bit more money, the 760 GTX is the best way to go.
If you're looking to save a bit of money your basic guideline should a card that almost matches performance of 7950. The 7870 is still a very good graphics card, I won't deny that.
Take a look at this if you haven't:
http://techreport.com/review/23981/radeon-hd-7950-vs-geforce-gtx-660-ti-revisited
It's not the raw performance from synthetic benchmarks you should be looking at, ff you're going to be gaming with the graphics card. They don't accurately reflect how the card performs in a game.