Depending on the games you play and the resolution of your monitor, they pretty much trade punches as to frame rate: http://www.anandtech.com/bench/product/519?vs=540
Power Supply-wise, the 470 is a 215W card, while the 6870 is only 151W. So the AMD would have the edge there if you have a low end PSU. http://www.hwcompare.com/8627/geforce-gtx-470-vs-radeon-hd-6870/
They both need 2 x 6 pin connectors, so be sure you have enough PSU for whichever you choose.