^ but in the hands of overclockers, 7970 led or at least tied from day 1. Only few cards like MSI Lightning 680 max overclocked could approach or beat a 1.2Ghz 7970. Once driver updates kicked in, 7970Ghz beat the 680 by June 2012 and held on to that lead until Titan in Feb 2013. 5870 only had the lead for 6 months.
As a gaming card, the 7970 is way better. It overclocked better than a 5870, came with 3GB of VRAM while 5870 became VRAM bottlenecked quicker, and in modern titles the 7970 is beating the 680:
http://gamegpu.ru/action-/-fps-/-tps/evolve-beta-test-gpu.html
7970 also came out near the peak of mining years where it produced a lot of valuable bitcoins, essentially making thousands of dollars. But, those who mined early on with a 5870 at lower difficulty but held on to the coins to flip them later, also made good $.
I would say both are amazing cards for different reasons but 7970 @ 1.15-1.175Ghz today is still relatively quick for 1080p at least. 3 years after 5870 came out, it was starting to show its age with VRAM and tessellation bottlenecks.