Wrong.
An oced 7850 is at par with an oced 580.
A 6970 is about 15% faster than a 6950.
A 580 is about 15% faster than a 6970.
An oced 580 is about 10-15% faster than a stock 580.
A stock 6950 is if:
100
Then
6970 115
580 Approx 132
580 oced Approx 145-150
So going from a 2gb stock 6950 to a highly oced 7850 is nearly a 50% performance increase. It is like going to a stock 7950 which is nearly 50% faster.
6xxx don't scale well with overclock, even if it is unlocked (higher clocks doesn't increase performance by much in this series), you are at most at 6970 stock performance despite a high overclock because of poor scaling. So going from 115 to 145+ is 30/115 so about 25% increase in performance.
No matter how unlocked/overclocked/both your 6950 2gb is, going to a 580 OC or 7850 OC will give you at least 20-30%+ performance increase and this will only increase further when games support more tesselation.
Going to an oc 7870 will increase the difference from an oced 7850 by nearly 10% more, so this means 35-45% performance increase.
An oced 7850 beats a stock 7950. And a stock 7950 is at least a 30-40% improvement of unlocked 6950.
However, it will vary with each game. But you will get slightly better playable settings or noticeably better gameplay, perhaps not both.
But you will consistently see a difference of 15-25% avg FPS increase in the worst cases and up to about 50%+ in good cases with average being around 25-30% or so.
And minimum FPS will probably see an even better benefit.
However, I will only recommend this upgrade if you are with Sandy or Ivy and not with previous CPUs nor with AMD.
Difference btw a stock 6950 and stock 580. If you want to compare 6970 which you have similar performance to, then compare the 6970 to 580 OC or near 7950 stock which is close to the performance you would actually get.
http://www.anandtech.com/bench/Product/517?vs=510
Avg performance difference is 20-50%+ which is what you are looking at.
Now, if we compare 6970 level performance to stock 7950 or within 5% of it: then:
http://www.anandtech.com/bench/Product/550?vs=540
The difference is too much to be believed. You may not see so much difference but this is beyond 50%.
I promise you a 20-40% increase in performance across the board.