Well an HD 6670 is very weak, and so at 1600x900 games will look better, sharper, and crisper than they would at 1366x768, but they'll perform worse. For FIFA 14 and Counter Strike: GO, you won't see a performance difference because you'll still be able to run those games at maximum settings and even if you went for 1920x1080 you'd still get above 60 fps.
Battlefield 3 is another story, though, because it's a much more demanding game. At 1600x900 on medium settings with 0xAA and 0xAF on Battlefield 3, you'll probably get around 30 - 40 fps average. If that's an acceptable frame rate to you, then without a doubt you should go for 1600x900. If that's not acceptable for you and 60 fps is your standard, you can still play at 1366x768 on a 1600x900 monitor, but the image will appear less crisp than if you were to play it at 1366x768 on a 1366x768 native monitor. It honestly shouldn't look that bad at all, though, and overall there's more benefits to have a 1600x900 monitor such as bigger desktop work space and such. Overall, it's a better idea to get a 1600x900 monitor, even if all your games can't play well at 1600x900.