OK, experiment #2. I'm going to forego looking at K values as it sounds like that may be confusing between reporting software.
Here's what I tried -- in a darkened room, I lit a subject by incandescent light only, so it had a steady temperature through the experiment.
First I took a white(ish) door and did a pre-set from it for each, labeled "D-1".
Then I shot 5 images of the same scene. I used an 200/f2 which IMO renders colors more accurately than any other I have. I shot in order:
Auto-1 Auto-2 Incandescent Forced Kelvin = 3750 (chosen at random to be similar to the light) Preset D-1
I did it with the D800 (top) and D4 (bottom).
The short version is that by eye they are all the same but the preset. The preset on the D4 is MUCH warmer (too warm). Since I don't use preset generally I am not too worried, but it is a bit strange.
But all the auto and the two forced presets (Incandescent and K) match.
Which is very different from what I saw outside. It's cloudless outside, let me go do something then. Though in doing this I noticed the fine tune is way off on my D4 and 200 -- off on a tangent for a bit to check it at more reasonable distances.