Originally Posted by
Dedweight
The two are fairly comparable, AnandTech as the 6950 edging out the 6870 by a mere 5%(usually less), if money is a concern the 6870 would be more than enough, if not the 6950(1GB version) would work. As for the 1GB vs 2GB question, the 2GB version is great for resolutions higher than 1080p or multiple monitors, seeing as you use 1080p 1GB would be plenty and might save you a couple bucks.
For reference I use the XFX HD6950 1GB and have been able to max out most games at or above 60FPS at 1080p(games being Skyrim and Deus Ex: Human Revolution), the only thing I don't like about the XFX is that it's loud and runs fairly hot(would love to drop it's temp a good 5C).