In a first test I made largely to see how easy it would be to take comparable images, I did throw a color-checker card into the scene, and in daylight, after finding basically comparable exposures and then adjusting the remaining .11 EV difference via exposure.
Executive Summary: The 1Ds3 and D800E, using RAW/LR 4.3, produced excellent and almost identical results on a color checker card.
Test: I made a number of exposures on each camera and picked two very close together (.11 EV separation.) It was very easy to bring the neutral line into close proximity with simple white balance and exposure adjustments. Once that was done, the vast majority of the patches also aligned quite well.
The patches that did show a difference in A/B comparisons were:
Patch 8: "Purplish Blue": Very subtle, the 1Ds3 result is slightly bluer, the D800E slightly purpler
Patch 11: "Yellow Green": D800E slightly warmer
Patch 17: "Magenta": D800E slightly more saturated
Theories that these could be explained by differences of warmth, red value or exposure seem belied by the other patches, which are pretty dead on, including the skin tones--where differences in red and exposure are often enormously visible.
It's difficult to tell if this represents very subtle differences in the camera profiles, my particular models of camera, or what, but the key thing to note here is that the differences here are quite minor. From having watched folks play X-Rite's color game and Blendoku, I would guess that many photographers would find at least one of those three differences imperceptable and the other two barely perceptable. These differences would be lost in the noise of white balance adjustment of a natural scene.
That having been said, if you're in the business of fine art reproduction under controlled lighting, and you forced me to make a choice, I'd probably give the Nikon the nod.