Tricky question. As stated above one of those at the moment is the fastest. However two of cards from either brand are in some cases much faster/capable than just the one and possible cheaper also. I.e., two 570s or two 6970s or ever lesser cards from either brand. Personally I would stay with either the 500 series from Nvidia or the 6000 series from AMD depending which your motherboard will support. I myself at the moment have one 6950 unlocked to a 6970 that works for me very well. I am thinking about another of the same card just for over kill sake as the single card is doing everything I ask it to. My two 6950s hacked and now 6970s are equal to and superior to one of the dual chip cards for about $450. You could get one card use and assess it for awhile and then if you please get a second.
Here's what Guru3d says in the conclusion to today's review of the Gigabyte GTX 580 SOC:
"To date this is the fastest GTX 580 we've had in our hands, and in fact this is the fastest single GPU graphics card tested to date. Now we tried to nitpick and look for small subtleties that could be better, but quite honestly, there isn't much worth even mentioning. We came up empty as all negative variables on this product seem to have been ruled out." http://www.guru3d.com/article/gigabyte-geforce-gtx-580-...
I would stay with the 500 series Nvidia or the 6000 series AMD and I admit I am partial to AMD. So for me two 6950s bios updated to a 6970s. AMD just released a new driver package the 11.4 and it is reported that it has improved the performance in some games quite a bit. Like 15% in Black Ops. It would depend which your motherboard would support, sli or Xfire.
If you are doing video editing and recoding, there is one new consideration in the mix. The Z68 platform arriving soon with its VIRTU switching will boost whichever GPU(s) you sellect.
Both platforms, AMD and Nvidia have their strengths & weaknesses. AMD is currently the speed champ with the 6990 which has 2 GPUs on a single card (like the GTX 590) which would save you the hassle of doing SLI or Crossfire. two AMD 6970s Crossfired or two GTX 580s SLI'd are (is) a strong graphics platform. But when using more than one discrete GPU you run into power and heat considerations that are greater than a single GPU.
If I were building a SLI or Crossfire system I'd want 1000W; but with a single GPU (even the 6990 or GTX 590) would need only 850W, and preserve a slot for later use.
While not as powerful as a GTX 590, my two GTX 560Ti's perform amazingly well in every game I have (BFBC2, Crysis 1 and 2, COD4 MW, MOH, and Metro 2033). The best part is you can get two 560's for less than the price of one 580 and will easily beat it in performance....