So just to get some dates in there for the whole this card competed against this card crap. HD 5870 was launch in Sept 2009, the GTX 480 launched in March 2010, these were both companies first dx11 architectures. The HD 6970 launched Dec 2010, the GTX 580 launched Nov 2010, this puts there second gen refreshed gpus in close competition for launch time. The HD 7970 launched Jan 2012, the GTX 680 launched march 2012.
The closest competitor the GTX 580 had from AMD at launch was the HD 6970, they were pretty close in performance, Nvidia could pull higher frames from certain games over AMD but did so with an additional 75-100 watts of power, the 6970 tended to overclock better as well. The HD 6970 got a driver improvement through 2011 that closed the performance gap (AMD has a tendency to do this), it was always more power efficient. In today's world the Fermi architecture wins (in the sense of whether you should buy it used or not) simply because nvidia still supports it with drivers, the HD5xxx and HD6xxx gens lost driver support at the end of 2015/early 2016.