You'll be able to run many games on "High" settings, just don't push the AA or the Antiscopic filtering too far. 4X on the AA and 6x on the AF and you'll be great, if you OC then you can bump those up of course.
You have enemies? Good, that means you stood up for something.
The 660 is much nicer, but you should be fine with your 650. I can run any game I throw at my PC on max settings on 1920x1080 reso just fine with my 660 (that I just got for Christmas ^_^), but you should be able to do almost max settings with most games with the 650.