I somehow am skeptical, having both bodies.
For a comparison, the d800 images should be downsized to 22mp as well - it's like the Canon aps-c 18mp vs 15mp vs 12mp sensors: While more mp might have more noise at 100% crop, downsizing them gives the newer sensor an edge. So more mp are there if you need them, but there's no real disadvantage iq-wise. But of course all reviews show that the d800 is not made for shooting at iso6400+, and wedding photogs are able to stay at iso1600/iso3200 mostly anyway.
Yes, turn my 36mp body into a 22mp body in order to make it look better. Thats how DXO rationalizes the high per pixel noise into something usable. Maybe if they resized it to one pixel it would be perfect.
The point is that there is no holy grail, and all the posting being done by those who just read articles and have zero experience with either camera is not very helpful.
Obviously, my D800 can take some amazing images at ISO 100 - 400, but just like the OP notes with his 5D MK III, as soon as you get into shadows and the ISO gets up over 400, you have to be more careful with exposures, and at very high ISO's, the 5D MK III has more DR than the D800.