The one and only time I had to use a towing service through AAA was a complete clusterfuck. My truck is AWD and I made it well known and that I needed a rollback. The contracted tow company took 3 hours to get a roll back to me just 10 minutes down the road from their station after sending two standard wreckers and one smart ass yankee just to determine that I had to have a rollback. The guy in the rollback finally made it and showed me where their order stated the truck was AWD and requested a rollback.
When my diff grenaded I talked to the driver after waiting 2 hours. The contracted companies deprioritize AAA calls because the make less money. So you get a tow when someone is available or at the latest the AAA contract says they can show up.