So, it seems, yet again, a bit of clarification is in order with respect to our latest Canon / Nikon flame fest.
First, all that white balance does is set linear multipliers for the individual channels. In order for a physical object in the real world to appear to have a neutral color under all light conditions, it must equally reflect all wavelengths of light equally. Most objects don't, which is why they have color. But a few objects, including some common and inexpensive ones, do. PTFE / Teflon does; get a roll of thread tape, and anything that appears to be a different color from it isn't white. (If it looks brighter, it's got fluorescent whitening agents added to it -- very common with papers and fabrics.) Tyvek (a common material for un-tearable envelopes) also shares this property. Polystyrene / styrofoam does, as well, but it's not quite as bright as the other two.
The spectral distribution of the light itself varies, and almost always even varies within the scene itself. There's much more blue in outdoor shadows than in direct sunlight; to understand why that's the case, look at the sky. As a result, a white object (such as a piece of PTFE) will result in an image recorded on your camera with a much higher ratio of blue to red and green when photographed in the shade than when photographed in direct sunlight.
Your eyes and brain, however, are wired to automatically re-interpret those color shifts on the fly, and the general perception is that the objects are the same color regardless of the actual light you're viewing them in. But, with a bit of practice, you can learn to see the differences in color from different light sources. And, for artistic effect, there's a lot to be said for slightly skewing your white balance in the direction of the actual light of the scene -- but that's another matter.
Most light sources are black-body radiators, and the color of the light emitted by a black-body radiator is very predictable and associated with a temperature. Heat something to 8,500°F (well past the boiling point of everything that comes to mind as I type) and it'll produce a glow very similar to sunlight. Heat it to a mere 4,000°F, which is what happens to the tungsten filament in an incandescent bulb, and you get the much redder color we know so well from indoor lighting.
When you set your camera's white balance to a color temperature, it uses a built-in lookup table (or whatever) to know that an object heated to that temperature will radiate light of such-and-such a distribution of colors and that, if the camera multiplies the three channels by these factors, they'll render neutral objects with equal RGB values. The catch, though, is that there aren't any perfect black-body radiators; though many objects are very close, all will have various bumps and dips in their spectral distributions.
But not all light sources are actually black-body radiators. Sodium vapor street lamps, for example, work by a completely different mechanism and only produce a single frequency of yellow light. Fluorescent lights work on a very similar principle, except they produce more frequencies of light -- but, again, generally in a pretty spiky distribution.
Your camera again has some pre-set values for some common light sources that again tells the camera to set a particular combination of linear multipliers that will result in a neutral object being rendered with equal RGB values. The catch here is that there's even more variation with non-black-body light sources.
That's where the manual white balance comes in. The idea is to take a picture of something that actually does have a flat reflective spectral response, and the camera calculates from that picture what multipliers are necessary to render it with equal RGB values. This gets you the closest of common methods, but it again has a catch: most objects that people use for white balance aren't very good candidates. That QP card that Mikael so loves to flog is a great example. For one, it's way too dark, meaning that the sample that the camera measures is going to have to average out the noise in the signal. That's especially a problem at higher ISO settings. But, worse, I'll bet you lunch that it doesn't have anywhere near as flat a spectral response as a $0.01 styrofoam coffee cup. Those things actually make far superior white balance targets to anything you can buy for less than a thousand bucks. And I mean that in absolute terms, too -- not just price / performance.
In the real world, though a coffee cup can get you very, very close to a perfect white balance, the only way to actually get it truly perfect is through ICC profiling in a process much too involved for me to discuss here. But the idea is to shoot not just a single target with a single color that's hopefully white, but rather to shoot a chart with a great many colors and to let special software calculate the various distributions of everything to figure out the actual value. Think of the difference between LensAlign and FoCal for an analogous comparison.
So, it's very reasonable to expect minor differences between white balancing algorithms from different cameras, especially considering the differences between sensor designs and what-not. But it's not reasonable to expect those algorithms to differ by more than a minor amount, and Nikon cameras are notorious for royally screwing up white balance in exactly the way the original poster has discovered. I'd go so far as to suggest that the cameras are unacceptable as shipped, though the problems should vanish in an ICC managed workflow.