Ive used both the AA & RAC over the years, and find the AA are better at actually TRYING to fix it rather than just tow it away. It just depends on how decent the engineer is on the day. Ive also tried the 'included breakdown cover' with insurances in the past, and find the people they send out are just toe rags with a low loader, that don't even want to bother getting you going, just take it to a garage. I use the AA to more or less tell me what the problem is, then get someone i know to fix it or do it myself.
I wonder if you chose AA personal cover, on a car that will cover you in ANY vehicle may be a way around it?