I'm sure there are tales to counter this but...
A VW Golf fell off the road in the snow. Two Occupants, one with all singing, all dancing AA cover, the other with All singing, all dancing RAC cover. The AA wouldn't come out, as for some reason it wasn't the right kind of accident. The RAC came out, but did say there would be a surcharge if special lifting aparatus was required.
I also understand - please correct me if I am wrong - that the AA operate a "Relay" service if the car breaks down miles from home - relayed from one recovery company to the next until they get you home, and this can mean sitting out in the cold with a broken down car for each leg of the journey. The RAC will get one company to take you the whole journey where-ever possible.
On the basis of this, I'm with the RAC.