I have both the cards listed above. I know that thr 7870 is clockd faster and has 2 gcs of memory. The other card is aower and only has one.

I assume both will play Skyrim at least ok. I problem is this: I

Your card list is not included in your post.

If you're going to use HD textures in the game, use the 2 GB card. The 1 GB card will not work well with these textures.

I don't see the other card...but go for the 2GB video accelerator for sure !!!!! (...and not only because of skyrim, many other games depends on that VRAM as well.)

People, tags are not a good place to put vital information.

OP, part of your post seems to be missing. I assume you have issues with the 7870 which is why you're considering using the 6850. Otherwise the 7870 is better in every way.