I tend to agree with Squilliam. Let's say in a perfect driver situation a HD3870 is about equal to a 8800 gt. That means it's also twice as powerfull as a 7800. A HD4870 then is 2 times the power of the HD3870, wich makes 4 times the PS3 gpu. The 5870 then is twice a HD4870, bringing the total to 8. Then finally the 5970 is a dual 5870, wich brings the total 16. So by that logic it would actually be about 15 times as powerfull as the PS3 gpu.
Than you have two side to look at it:
1: This is an ideal situation, so the number is probably lower, say 10-12 times as powerfull.
2: We have not counted in the DirectX revisions, since the HD5xxx series is two Directx gens ahead of PS3. Also the architectures of modern gpu, like the unified shader parts are still not fully utilizied, and also offer more potential power than the old pixel pipeline architecture of the PS3 7xxx gpu. This making the number higher.
Then on a side note the HD consoles have proven to be mostly memory limited, especially if one would like to use 1080P in games. The 2048mb ram of the HD5970(1gb per gpu) completely removes this limitation.
To sum it up, i would say 12 times more powerfull is actually an understatement, and i would say closer to 15 times more powerfull in a scenario where it's full potential could be utilizied, wich a gaming console is since all the PS3 have te exact same hardware.
