Meh been with the RAC for years and have called on their services (flawlessly) many times. Fact is if you go digging you can find horror stories for any firm.
Didn't need to dig, 9/10 threads on their forums are complaints.
People don't post when they've had a good service though.
I used to work for both, for my own cover I went with the RAC, mainly as got a better deal for the family, and the AA don't attend if you have an accident( or they didn't).
One example I had with the AA, they recovered a customers fiesta diesel to my garage, was told the timing belt was snapped, after I talked to the customer he told me the patrol man asked him to try to start the engine while he was spraying something(easy start) into the air intake, the engine went bang! After I fitted a new head we sent the timing belt to the AA, as it had clearly snapped clean through, they sent it back saying the teeth had failed
After I'd done the job it wouldn't start, it was out of fuel