I have cancelled the renewal with Green Flag and subsequently looked at reviews of both the AA and the RAC and from what I've seen so far leaves very little to choose in terms of response and recovery.
It does seem that it depends on what you're broken down with. A simple thing like a jump start or wheel change that can be sorted at the roadside and it's fair enough.
Anything more complex like a mechanical failure, and you're waiting for an onward tow or full recovery truck. And that's more of a lottery as to how quickly you'll get home. It seems apparent that all recovery services will sling-shot you between private recovery firms if you have broken down and you don't live in the area they cover.
If you're involved in a collision and the vehicle isn't driveable, you could wait some considerable time as roadside repairs seem to be prioritised, unless you're on a motorway or the vehicle is causing an obstruction. Generally in those situations either the police or the Highways Agency patrols will drag the vehicle to a safer position.