I used the AA years ago, my MR2 had stopped working over night, the guy turned up, put the key in and had it ticking for 5 minutes until my throttle cable was smoking! The earth strap had a bad connection so the current was finding the next best ground... all that needed doing was cleaning the earth strap connections but the guy had to tow my car to a local garage - useless! That was quite a few years ago mind.
Never had a problem with RAC, they've been pretty solid when I've needed them. Not sure if it's still the same, but the AA didn't include vehicle recovery following an accident where as the RAC did. If that's still the case I'd decide on that alone, the last thing you want after bending your pride and joy is another bending on the financial side for towing your car somewhere safe.
No idea about green flag or others, you'd like to think they've got so much competition trying to break in to the AA/RAC space that they'd go above and beyond to do it... but then I guess less customers means less money so maybe they can't.