GTX 560 and the HD 6870 are close in terms of performance. At times the 560 wins and at other times the 6870 wins.
I'll take the HD 6870 for $130 because that's really cheap, considering it costs around $160.
Also, it consumes a lot less power than the 560.
$20 more for a 560 is tempting, but if you have the money for it, it can be considered as well.
GTX 560 review, with benches from HD 6870http://www.tomshardware.com/reviews/geforce-gtx-560-amp-edition-gtx-560-directcu-ii-top,2944.html
Also at what resolution are you gaming at?