I would pick The GTX560.
From a performance point of view, they are comparable.
If you will be playing just one game, then search out benchmarks for that specific game and make your choice.
Otherwise, nake your choice on other factors, like vendor, price, warranty, or familiarity with the drivers.
Personally, I prefer direct exhaust cooler types better.
The 6870 looks restrictive to me, and I like EVGA as a vendor with good USA support.