Yes Sir, the D810 is has an better image quality and dynamic range than the 5DIII. But, as you can read in many postings on this forum, an optical system is more than just the picture sensor. The whole system has to work perfectly together to help you to get an - technically seen - good picture.
In my family, you can find the D810, D800 (both my husband), 5DIII (my son), 6D &7 D (myself), and A7r (my daughter).
And each camera has its benefits. My daughter needs a light camera with an good image quality (like my husband does - but he owns several Nikon lenses). My son and I prefer to shoot birds, planes and animals, so we stayed with Canon).
The 5DIII is an all-in-one package. The image quality is not as good as the Sony´s and Nikon´s, but its autofocus system is superior. The D810 has an superior image quality, bit the autofocus system lacks of speed, if you shoot moving objects.
I think, each camera has its own field of application. Sometime you can not directly compare them betweeen.
I it true, that Canon should get better in resolution and dynamic range, but Nikon should hurry up to get an fast autofocus system. (This is my opinion).
By the way: My husband, who stayed at the soccer WM told me, that there were several modified cameras "in the field". With bulky housings, others with an odd combination of cameras and lenses or leneses that were not printed with their specifications). So you can be sure Canon is working on succesors of the 1Dx and 5DIII.
From my experience of handling Nikon and the newer Canon lenses...is that Canon's lenses are several generations ahead of Nikon. Nikon may make the finest resolving SLR on the planet, but their lenses are not able to match or exceed their sensor tech. Where as with Canon, their lenses are far out resolving their sensors.