Ok, so did my tests. Not quite as scientific as yours, but I think fairly close. I have the 5d2 and 5d3, tripod against a piece of white paper next to some lights, so OK lighting. First shot was AWB and used that to set the custom WB, and took a 2nd. Pulled all 4 photos into LR4, and looked at the color temp & tint values, then took the 2nd shot and approximately the same area, used LR's WB dropper.
Shot 1, AWB: 4350K, -2 tint
Shot 2, Custom: 4200K, -5 tint
Shot 2, LR Custom: 4250K, -3 tint
Shot 1, AWB: 4650K, +7 tint
Shot 2, Custom: 4650K, +6 tint
Shot 2, LR Custom: 4650K: +6 tint
The output on my screen (high quality TN, 95% NTSC calibrated panel) looks pretty darn close to each other, even though they are off by ~300K and 10 tint, more or less. Both cameras have, at one time or another, been through CPS for cleaning/servicing. So, I'd reinforce, it's sensor/electronics differences that is the difference, and not a problem with either camera. Don't worry about it, it's all just fine.