AA programs are all in concert with a university medical school, with a board-certified anesthesiologist serving as the medical director for each program. They do their clinical time with anesthesiologists and other AA's. Depending on the school, they may take a few classes with medical students (physiology for example) or with other PA students. AA students are exposed to all subspecialty areas in the OR, including peds, neuro, and cardiac. Their first year is primarily didactic, with some OR time. The senior year is mainly OR time, with a few conferences to attend each week either in person or via web chat if at a remote clinical site.
CRNA programs are generally tied in with a nursing school, and with two exceptions that I'm aware of in Florida, have a university affiliation that allows them to grant an accredited master's degree (or DNP). The bulk of their training is generally done by other CRNA's, but there is a lot of variability from program to program. Military CRNA training is generally recognized as one of the better programs. Interestingly, the move to the DNP increases actual clinical training very little, if at all.