The reason nVidia is faster in civ 5 is because Civ V is the first game to use DX11 multi-threaded rendering. It's a single Dx11 feature. It doesn't mean that as other Dx11 features are utilized that nVidia will be faster. It only means that nVidia is faster with that one feature only. You can't extend that to any other features. I'd be surprised if AMD doesn't pick up multi-threaded rendering, as well. Time will tell.
What about DirectCompute? Looking at the Civ V, Nvidia also has the edge in DirectCompute texture decompression, but I'm not sure if thats due to the multithreaded drivers or not.
The Fermi architecture does seem to have greater computational abilities overall though.
Remember though that it's only one game that currently uses it. Do you know that Crysis 2 and BF3 are going to use it too? If not then you can't say nVidia will have any advantage in those games. Eventually I would imagine other games will use it, just as I imagine AMD will support it as well.
I'm certain BF3 will use it. I remember reading a quote from a BF3 dev lamenting the fact that at the time, neither AMD or Nvidia supported multithreaded drivers. Now that Nvidia supports it, I'm certain they will implement it in their game.
As for Crysis 2, I don't know, but I hope it will support it. Nvidia had a hand in the DX11 development, so we'll see.
Keep in mind too that the 570 is limited to 1gig of VRAM, when you are suggesting it will be better in future games. That could very possibly kill it quick if games demand more RAM. We are on the cusp in some games now. More than just one game using multi-threaded rendering.
The 570 has 1.28gb, which is enough for the resolution the OP plays at. The 6970 is definitely more future proof in that regard however, I'll not deny that.