The AA and the RAC both have their own patrols, who try to fix your car at the roadside before considering anything else. Other companies, such as Green Flag and Autonational Rescue use local contractors, who're far more likely to turn up with just a tow truck to get you to their garage (or, if you've got 'relay' cover, to your destination, still with your broken-down car).
I'm not knocking Green Flag, Autonational Rescue, etc. (I was with Autonational Rescue for years). However comparing their services to those of the AA and RAC can never be on a true 'like for like' basis.
I'm currently with the RAC because I get a good deal with them through Post Office Insurance.