You will not see a performance increase, in fact you will likely see a performance decrease in those specific games.
I agree, the 6950 is a step down in terms of performance, and the 1GB version gets the same benchmarks than the 2GB version in 90% of the benchmarks because the extra ram doesn't help except on extreme settings.
Even the GTX 570 is considered a sidegrade from the 480, as they are very similar in design.
If you are going to upgrade, the only decent boost that justifies the money, IMO, is at least a 580, and perhaps two 570s or two 6950s.
I'd personally want the 6950 over the 480, only due to the noise levels. If you unlock the shaders of the 6970, they'll perform very close, but the 6970 is quieter. It's a worthwhile trade IMO. Just as long as you realize you won't be upgrading performance.