Some people have a preference of registry, and it may depend on which registry has shows in their area, or more shows in their area. Some like me may have both under 34" and over 34" to 38" miniatures and it is more convenient for us to go to AMHR shows where we can show both sizes at one show. Some may have more friends showing at a certain registry. We used to show both AMHA and AMHR shows, the more shows the better was our motto back when we had lots more energy, lol!
I suggest that if you have access to shows by both registries, attend both, see which you prefer. Your preference (if you develop one) may be for the different style of one show committee over another, rather than anything having to do with the registry itself.