I've found that in most instances, AAA beats AP rates for concierge rooms. When you think that AAA is a percentage off the total cost of that room, while AP is just a flat amount off any room, AAA generally works more in your favor.
I know this held true for our room in the Royal Palm Club at the GF last month. I secured AAA for it months out, and when the AP rate came out, my TA e-mailed me that AAA was indeed still the better deal.
I was able to secure a AAA rate at the AKL club level for mid-December next year, and know I could also do the same for club level at the GF for afterwards (have a regular room there, and trying to decide if I want to splurge again!).