If you are overclocking, the 560 has loads of headroom, the 6870 has very little. Overclocked, the 560 is consistently better, at stock they are pretty much the same. The 560 comes with PhysX for those Batman, Metro, Borderlands, Mafia, and Unreal Tournament games.
Very safe. Most cards come with a factory overclock aready out of the box. When you do regular overclocking without adjusting the voltages there is virtually no risk whatsoever. If you push the card too high, you will likely only get on-screen artifacts, at worst the card will crash and you simply need to re-boot the PC to reset everything.