As a professional who has shot cars and trucks for car makers and their agencies for over 25 years, let me say that it is highly unlikely that there would be much if any difference in the color rendition of the two cameras had the color of the lighting been identical. As others have already pointed out, the color of the cloud bank reflected in the windshield of the 5D3 is obviously hugely warmer than the clouds reflected in the windshield of the 1DX. There is no question in my mind that this accounts for the vast majority, if not 100%, of the color difference.
At sunset, when clouds across the horizon are moving quickly, dissapating due to weather front movement or, more likely, atmospheric cooling that reduces the amount of evaporated water vapor in the air, the sky color often changes very rapidly as the very warm (low color temperatrure expressed in Kelvin degrees) source of light from the low-sky direct sunlight may be revealed as it peeks out between low hanging cumulus clouds, or is revealed as the clouds covering it are thinned out or disappear entirely. If you look at the reflection in the 5D3 windshield, one can see this effect in the reflected clouds which have obviously been lit by much warmer light from the setting sun. This is all very clear from the examples.
As to the color noise, it was also very much affected by the color temperature. The "grain" size and frequency of the noise was obviously affected by the warmer color light; because the subject was much warmer (redder) in the 5D3 shot, it was recorded much more heavily in the red channel, the channel which always reproduces much more noise than either the blue or green channels. This is the same reason why images lit by low light tungsten lighting are always noisier than those lit by low light daylight-colored light sources. You can easily see this by the vastly greater number of red noise clumps in the 5D3 shot, making the image look more "noisy" than the image from the cooler (less red, more blue and green) lit 1DX shot.
To summarize, the color rendition issue is probably due entirely to ambient color temperatures at the time of each shot, and the noise differences are probably almost as much due to the same influence; without the color change, the 1DX probably would still have had less noise, but only a tiny fraction less, and the noise evident on the 5D3 would have been of the same general color range as visible in the shot taken with the 1DX.