Carbuff - I've never run out of juice and had to be towed. However in four years of ownership, I've had an FFE towed three or four times to the dealer, and once after buying a used one. AAA has never had a problem. In fact the drivers usually love the challenge and are fun to talk with.
If you are not a AAA member, there are three levels of membership. Classic is 4 tows per year up to 5 miles each. Plus is up to 4 100 mile tows per year. And Premier (used to be RV) is one 200 mile tow and up to three 100 mile tows.
They always provide jump starting for free. That is a really useful thing if you can't get the car in neutral and don't want to read the manual on how to manually get it in neutral. And sometimes the jump start will get your car running, and they will typically follow you to the dealer if it isn't too far away.
The AAA card is for the person holding the card, not tied to a car. So you can help anybody as long as you have the card - they don't care which car you have towed.
When you call you have to ALWAYS request a flat bed. If you don't ask for a flat bed, they will send any tow truck. The owner's manual specifically says, no towing with wheels on the ground. (there have been tons of debates about that issue here - that's what the manual says, and that's what I stick with when towing).
They will tow the car anywhere you tell them to tow it. There is no rule about towing to a AAA location, or a garage, or a where ever. You give them the address, if it is within the range you purchased, they tow it for free. If you go beyond the range you have purchased, the driver charges you by the mile. It can get very expensive, very fast.
Some drivers allow you to ride along, some have some weird rule about no ride along. I now know to ask up front, can I ride along - if I need to ride with the car.
I've had AAA for a very long time. Had many cars towed by them. It is well worth the insurance.
Ford road side assistance uses the exact same tow trucks as AAA. Ford has stricter rules about where they will tow the car. I think it will only tow to the nearest dealer. There is no mileage limit. And I'm not sure they will try to jump start your car. The contracts are different, they just use the same pool of tow trucks.
You'll rarely see a AAA tow truck (there are pickup trucks that will deliver batteries - AAA batteries, how those small cylinders are useful in a car is beyond me). They contract independent tow companies to do the work.