>>89377713 year elevator mechanic here.
hex are all around the best. you have the option of using a wrench or a driver on a power tool. if it's totally wrecked, you can cut new flat sides into a head and grab it with vice grips. hex head is the best option when dirt/rust is expected (e.g., outdoors or wet locations). every other head type becomes completely unusable.
i really like torx. i like the way it doesn't cam out when using a power tool. when using hand tools, torx don't round off like allens do.
robertson can fuck off, and so can most pozidrive/phillips. flat head is fucking obnoxious to deal with and i throw them out and replace them with something sane at every opportunity.