You must mean the 6870 was defeated by the 580, because the 6970 isn't released and hasn't been reviewed yet so we don't know what it will do. And the 6870 isn't even as powerful as a 5870. It's more like a slightly beefed up 5850. So no real surprises that the 580 is best right now.
Anyway to answer the question at hand... well there's a lot of variables. Of course more ROPS is better. So is more speed, so is a higher bit rate, and so is more CUDA/Stream cores. It's pretty obvious. Now since you're focusing on rops, well again, 64 is going to be the best unquestionably, but 32 is totally fine as well. Having a higher bit rate along with it is very imporant too, to be able to quickly address the VRAM. And with that, more VRAM is at times going to be of the most benefit, depending on the game and resolution/settings used (AA, AF, DOF etc) because there's a lot of nice options that will eat VRAM up. My 1GB cards feel lacking at times.