We have had AAA for more than 20 years. We've never had Good Sam's Club. A previous poster let the cat out of the bag when he revealed that it is likely that the same guy is going to be coming to your rescue no matter which company you call. I suspect that this is especially true the more off-the-grid that you wander.
I've personally called AAA many times for jump-starts, flat tires, and breakdown towing for my personal automobiles. I haven't yet needed to call them to help me get my AS out of trouble. The only thing I will complain about is how long it sometimes takes to get help after you've made the call. I've decided that it just makes more sense for me to change my own tires, but I'm thankful that my wife can use the service if she has a blowout while she if off driving in another vehicle.
The AAA TripTik and all of the mapping documentation is arguably the best part of AAA. If you join them give the TripTix a try before you take your next trip. It is a wonderful resource to have available during your adventures.