I recently built a computer, but I don't have a graphics card yet. I'm looking for something cheap (around the $120-200 range), but can still play modern games with pretty good performance on a single 1080p monitor
If you like PhysX in your games, then pick up a 560Ti. Otherwise it really depends what games you're playing. The 560Ti 1GB beats the 7850 2GB in some games, but not majority. I personally like Nvidia because I like getting updates often to improve performance on newer games (and because of PhysX)
I freaking love FXAA on my 560Ti. I switched to FXAA in Skyrim the other day from using 8xAA, and now I get like 20 more fps and the game looks just as crisp :) therefore it's definitely the best thing ever
Radeon have MSAA which is the best looking, but also the hardest hitter on your framerate. Only the bravest people with serious Radeon horsepower dare to turn it on :)