Do you mean 560 ti or 560?
The 560 ti is the easy choice over the 6870, but if you mean the GTX 560 then they are close in terms of performance.
I would give the slight edge to the 6870 as it typically has higher minimum FPS and lower power consumption.
Plus, the cheapest 6870 on the egg is $155 after MIR compared to $175 after MIR for the GTX 560.
6870 - $155http://www.newegg.com/Product/Product.aspx?Item=N82E16814102948
560 - $175http://www.newegg.com/Product/Product.aspx?Item=N82E16814130660