I have been with both AA and RAC, and found that tha AA are better at fixing breakdowns at the roadside, the RAC tend to tow you to the nearest garage.
Example:- The Izuzu I had split a heater hose, the RAC towed me to a garage to get it fixed.
A VW passat I had split a Diaphragm in the Carb, The AA came Diagnosed the problem, said back in a few mins.
Came back with new Diaphragm, fitted it and back on the road