Well the 5870 performs better in DX9 and in a lot of DX10 games but the HD6870 is generally better in DX11 games because it has access to morphological anti-aliasing and is better at tessellation.
In terms of the 3 cards being discussed it depends what feature of a GPU appeals the most:
Performance: (best)GTX560Ti > HD6870 > GTX560
Power consumption under load: (least) HD6870 < GTX560 < GTX560Ti
Heat: (least) GTX560 < GTX560TI < HD6870
