I agree with Sanso,
The quality of the teacher is more important.
But I like to add that the teacher is only partly responsible for the result. Half, if not bigger, is determent by the quality of the student.
On Deeper Blue an article appeared detailing this quality that is highly dependeble of attitude of the student.
Though I have not followed an AA course, but took two AIDA's as it was the only choise for me at the time. I've talked to AA instructors. In generally I have the impression that AA is more centerd about feeling and style, and AIDA's course a little bit more geared to performance and competition.
I think if you already have a prefered look on your way, I think you can ask your AIDA instructor to match his course to your 'recreational' nature, or ask the AA instructor to have more focus on the competition part of freediving.
Have fun with your course, and bring a buddy so you can train safely when your back at home!
Love, Courage and Water,
Kars