It depends on what time of year you go and what resort you are staying at.
AAA can get you a discount on the room rate only with the purchase of a package. If you purchase the package through Disney, you will not receive the AAA rate. We went last year during value season and stayed at a deluxe resort (WL) and saved about $200 (roughly 10%). AAA is great for other discounts too -- not just Disney. We save on hotel stays, dining, and oil changes at various places. It really paid off the 2 times my DH locked his keys in the car! Well worth my $72, believe me!