Ultimately the differences between AAs and CRNAs may all boil down to one single difference, and determined by the name "Anesthesiologist Assistant." (You can not be an AA if there is no MDA around.) However, until all the states get some sort of practice act together for AAs and try for some standardization, you will see many differences. For example, one state may say AAs can do epidurals, another state may say they can only be the "anesthesiologist's assistant" and help the MDA put them in. I think a lot of the arguments come about because of the yet undetermined (by most states) role of the AA.
In regards to the AANA, years ago when the Nurse Anesthetists formed there own national organization, the American Nurse Association did not like it and wanted the ANA to be the only nurse organization so they basically "kicked" the Nurse Anesthetists out. I see somewhat a similiar thing happening now. The AANA in order to protect its members is fighting against the AAs. Yet the AANA is the first to admit that due to the shortage of nurses, there is a shortage of Nurse Anesthetists. Perhaps the AANA should combine with AAs, taking them under their wing, and start using its power to PUSH for AA practice laws in all the states. If AAs are given the same licensing standards and offered the same professional recognition, maybe we can have a little more peace in the anesthesia world. (I will now be tried for treason by my fellow CRNAs)