For rigid body alignment all tools should work well as long as they get a good starting estimate. Rigid body registration is very constrained, so the opportunity for subtle local errors is small. If the algorithm has a poor starting estimate, these algorithms will fail catastrophically, and you can see that easily with visual inspection of the results. If they have a good starting estimate, one will get a virtuous cycle of the algorithm homing in on a good solution (within the limits of the method).
When we first acquire MRI scans, the origin of the image will be the scanner isocenter, and the world coordinates will be with respect to the scanner bore. Therefore, you get a lot of variability depending on how the individual was positioned in the head coil. You may want to consider a method that uses center of mass and other heuristics to set the origin and alignment to roughly match MNI space. As an example, consider my setOrigin scripts. This will provide nice alignment for other methods.
Using rigid body coregistration will align multiple images from the same individual well. You can then look at non-linear deformations across those images to understand atrophy. However, those comparisons will only be in the individuals space, and make group inference a bit trickier.
For doing longitudinal group studies like this, you might want to look at more aggressive non-linear deformations that align images from different individuals to standard space while modulating the tissue for the amount of deformation applied (in other words, if an individuals corpus callous had to be dilated to have an average size, each voxel in this region has less white matter, just like the way the surface of a balloon gets thinner as it is inflated).
The nonlinear normalization of ANTS, SPM, AFNI can do a terrific job fitting local differences, but they can also create very subtle and hard to detect errors. In my experience, they all do a pretty good job with healthy young adults with European ancestry. However, you need to be very wary of using them images from older adults, individuals with wide diploid spaces, individuals with post-bregmatic depression, etc. Since the ADNI dataset includes a diverse range of individuals who are older, you will want to be very careful pursuing a non-linear approach. Since I work with stroke in a diverse population, I have spent a lot of time developing in house solutions. However, the widely available tool that has impressed me the most is CAT. I have seen CAT do a terrific job on images that confound the standard SPM routines.