As others have said it may differ on area, and of course differ per instructor, BUT yes I went with the AA a couple of years back and am glad I did - I wanted to go with a big chain just because if I had a problem with the instructor I could complain to their boss, rather than them BEING the boss!!
But I didn't need to complain fortunately, yes it's a tad more expensive but he was very professional and the car was fantastic (very new ford focus, was clearly looked after)...not some stupid little Corsa that I see some people learning in.
Also, I would recommend going for 2hr lessons. You may think that this is costly but especially in the earlier stages of learning your instructor will drive you to a more quiet area which may take 10mins or so up. In a 1hr session that's 10mins to place, 40mins learning, and 10mins to drive back.
If you have a 2hr session thats 10mins to place, 1hr40mins learning, and 10mins to drive back. So double the cost yes, but you get more than twice the actual practical time learning. And when you start getting better in 2hrs you can go for miles (and the time flies by!!).
So yes, AA was good, and 2hr sessions were a great idea.