The way a show gets it's rating is what classes are offered, and how much prize money there is
A rated is counting for better points than schooling shows and double A rated shows are counted for more points than A
Actually the usef dropped that rating. They are now national and premier shows.
A and AA shows are both governed directly by USEF. (in fact, if you are not a member you actually have to pay a non-member fee) whereas some of the B (local) and C (schooling) level shows are governed by USEF affiliated organizations or just the hosting barn's rules. Technically a show's rating comes from the amount of prize money given and level of classes. So typically an AA show would have a wider selection of classes with more prize money, which generally means that it will be more expensive! But I really don't notice a difference between A and AA shows around here. Actually most of the show "series" will offer anywhere from 2-6 weeks of shows in a row and some of the week are A and some of them are AA. Most people stick around for at least a few weeks. Our local (B) shows are run by a USEF affiliated organization and has no rated show classes (ie: they don't offer Childrens, Juniors, etc) but the rated shows around here offer the nonrated divisions (short/long stirrup, etc) on top of the rated stuff. NONE of the shows around here offer any kind of breed/registered classes. But unless you get into the A/AA scene a lot will depend on your location. If that makes any sense (sorry for the length)