Benchmarks seem to vary from game to game when comparing relatively even Radeon vs. Nvidia cards. Some games are more friendly to one, and other games to the other. A decent 7850 (one with a good cooling solution) can be clocked up a fair bit. Use caution overclocking video cards.
There will not be a massive difference from one to the other, AMD never surrender bundle giving you free games may make a 7850 more attractive to you.
http://www.tomshardware.com/reviews/gaming-graphics-card-review,3107.html
Link to Tom's best video cards for the money. This is your friend...
Sales and pricing in your local area will help make your decision. One thing I have found over the years, no matter what video card you buy, a better one will go on sale for less money next month. It's like a rule or something I guess......
Hyper 212, can't go wrong there.
I have always thought an all AMD build works better together, but benchmarks don't necessarily bear this out.
Search this website for Tom's testing of both cards, and keep in mind one company's 660 or 7850 does not always perform the same as another company's.
Power draw may matter if you are going to use the same psu.
I can say that the Gigabyte windforce card I have is fantastic for running cool. (See what I did there?...
)
It won't go above 55c for me no matter what I do to it. Including running gpu stress tests while overclocked to 1150 core/1400 memory.
Runs mid 40s C in normal gaming.
That is in a very well ventilated case with 5 120mm case fans though. So if your choice is budget driven and the performance difference is very little, I would say go for the one with the best cooling for long life and trouble free operation for a few years.
Various posters on the forums here seem to quote high-ish temps for the Nvidia cards, but maybe I'm just spoiled by one that runs very cool.