Actually, registration and registrationx *are* doing slightly different things under the hood. That's why the no-x version never disappeared as had I originally intended.

In short, the x-version was a more mathematically "correct" implementation of the multi-resolution algorithm. The original, non-x implementation had taken a number of shortcuts to speed things up when CPUs were still fairly slow. As an example, it would precompute histogram indexes from all pixel intensities (mostly for use with entropy-based metrics such as Mutual Information, but also used otherwise). It would then do interpolations on these indexes, rather than on the original intensities, thus saving the floating point operations that would have been needed to convert interpolated intensities to histogram indexes over and over.

Now, the x-version did away with all these shortcuts in the hope that it would deliver more precise results. Unfortunately, it turned out that it lost some robustness in the process, presumably because the aforementioned shortcuts had the side effect of smoothing the optimization problem and getting rid of some local minima.

So it's not unexpected that the two versions would give different results, with each better in some cases that the other, since that's exactly why there are still two versions in the first place.

All this pretty much applies analogously to warp and warpx.

I have a feeling none of this really helps anyone, but I am glad we finally got to talk about all this :)

Torsten