High ISO performance is nothing without low light autofocus performance

You're saying focus sometimes misses both in front and behind?

Let's start with the obvious: there could be something wrong with your AF. Could be dirt in the AF box or some other problem.

Assuming it's not that: Yes, no doubt that 36 MPs makes the error that much more obvious. However the good news is that unless you print bigger than before, the image does appear sharper as it's averaged down (magnified less). But coming from a D700, I would be very very surprised if you have worse AF with a D800. If you do, maybe you should have the camera looked at.

I think that the different CAM modules have different tendencies, and I've noticed this over time with switching between bodies. For example, I felt like the D3 had a distinct tendency to choose something towards the rear compared to the D2x.

One thing I felt like always made a big difference for me is mapping the size/location of the AF sensors. The kind of inconsistency you mention above makes me think that sometimes the sensor is wandering off the intended subject a little. I strongly recommend doing this. I won't lie: it's a pain. It takes time and it's tedious. But personally I won't shoot with a camera that I haven't done it with. And the more precisely and accurately you do this, the more meaningful the results will be. Make sure you have a good target that triggers the AF reliably and has good background separation.

Lastly, there is no substitute for actual testing. There is simply no way to using anecdotal or random evidence from real-world shooting to come to any sort of conclusion. Buy a lens-align (or make one) and get to it. And then do it again in lower-light conditions.

There are so many variables in real-world non-static shooting that variation is practically expected. But that variation is precisely what makes it hard to rule out a physical (camera body) problem or to learn the camera's tendencies.