That's subjective, Anandtech's GTX 560 review proves you wrong.
In Crysis Warhead, HD 5870 outperforms the GTX 470 and GTX 560 at all resolutions.
In Battleforge, the GTX 470 and GTX 560 outperforms the HD 5870 by 10fps average
In Metro 2033, the HD 5870 outperforms both at all resolutions except at 1680x1050 which matches the GTX 560.
In HAWX 1 at 2560x1600, the HD 5870 matches the GTX 470 and gets outperformed slightly by the GTX 560. At other resolutions, the HD 5870 is slightly slower than both.
In Civilization 5, the HD 5870 is slower than both at all resolutions.
In Battlefield BC2, the HD 5870 and the GTX 560/GTX 470 trade blows depending of the screen resolution, at lower resolutions, the HD 5870 outperforms the GTX 470 but the GTX 560 is faster, at higher resolutions the HD 5870 outperforms both.
In STALKER COP the HD 5870 outperforms both at all resolutions, albeit by a small margin.
In Dirt 2, HD 5870 runs slightly slower than the GTX 470 and GTX 560, at higher resolutions the HD 5870 outperforms the GTX 470 but still slightly slower than the GTX 560.
In Mass Effect 2 the HD 5870 outperforms the GTX 470 in all resolutions and the GTX 560 is slightly faster than both at all resolutions.
Wolfenstein the HD 5870 outperforms both at all resolutions by a consistent margin.
Source:
http://www.anandtech.com/show/4135/nvidias-geforce-gtx-560-ti-upsetting-the-250-market/1
Which means that the HD 5870 is faster than the GTX 470 overall, and the GTX 560 is essentially matching the HD 5870, sometimes is faster. sometimes matches it, which means that the GTX 560 has a very slight edge over the HD 5870 which doesn't justify its price premium over the HD 5870, the ATi card still a better buy overall.