Very good advice to see what shows are available in your area. Here in the southeast/eastern coast, there are many more AMHA shows available, so the "market" is more for AMHA horses. But many dual register with both registries, so as to have a market to people in different areas of the country.
The height requirements for AMHA is 34" and under, as was previously mentioned, and AMHR up to 38". So, depending on the size of the minis in question, that can also dictate which association a horse can be registered with.
I also agree, AMHR is easier to deal with and cheaper, but I'm here in Florida, so my horses had to carry both registrations in order to be marketable when I was breeding. Most all of mine were registered with both AMHA and AMHR, and competed in both the National and World shows -- sometimes depending on the height of the horse.
Good luck!