I went to their compare thingy (there's a link to their compare tool at the end of the last page). I changed out the 5DmkII for a D800, clicked on measurements, and looked at all the pretty graphs comparing the D800 and the 5DmkIII.

The only difference the graphs show is that there is more dynamic range on the D800 for ISOs under 800. For everything else, they're pretty much equal. The 5DmkIII even has slightly more DR at high ISO.

I'm not sure how this ends up becoming a much higher low-light value for the D800. Low light when using ISO 100 and long exposures?