From what i see XFX card is better out of the two for 1080p gaming. If your planning on overclocking the 560 would be better though, and the 560 also has PhysX which will add aditional visual effects to games that use it.
they are pretty close. it wouldn't matter much which you pick. the nvidia will have the option of physx and cuda for business use. the 6870 just happens to be cheaper. if you buying it on sale, the 6870 will be the money contender. if not i would use the 560.