3GB 580 is the better one but more expensive. The 2GB (I assume you mean the AMD 6000 series) is more affordable and can still play games with excellent quality, but not quite as good as the 580. In conclusion: yes, but for some higher quality games you might have to change some settings down a notch or two if you want to improve your fps but I doubt those changes will be anything drastic. From what I've heard and read (I'm only just learning these things myself) both the 6950 and the 6970 are of good quality and price.
But just buy the 580 if you can afford it.