Check several things:
How far will AAA tow it, I believe there's a limit on mileage where as GS will tow it however far needed to get it to a suitable repair facility.
Does AAA pay for the tow up front, or do you have to pay and they reimburse it? GS pays the tow company direct, nothing out of your pocket.
Will AAA pay to tow the truck with the TC on it?
I've used GS towing twice, both times with very good results. State Farm wouldn't tow my Class 6 tractor, even though it's insured with them, because they consider it a commercial truck. GS didn't question it at all.
Bill