Hmmm, good question.
My gaited experience is with TWH, Paso Finos, and Saddlebreds. However, I think there are some Appys out there that are considered gaited because they gait in what is called the Indian Shuffle. From experience, I've known some terrifically versatile Appys that have been able to do each and all of the afore mentioned disciplines very well, so if one owned an Appy that did the Indian Shuffle, I would have to say it was a good contender.
Secondly, after the Appy I thought of the MFT too, but I don't have any experience with them so can only speak from what I have read or heard about them.
Then there are gaited Morgans. Morgans as a whole (that ones I have known or owned) are wonderfully versatile and strong in all the disciplines with perhaps the exception of dressage.
I hear the Bashkir Curly (sp?) is a terrific horse that has a gaited off shoot.
While I like a bare footed TWH and think they excel at many things including some jumping, I'm not sure they would be near as strong in driving as a Saddlebred, which can also jump, but probably not as well as a TWH. Not sure typical Saddlebred conformation is geared towards scrambling over rocky trails either.
The Pasos I've known were pleasure horses with huge hearts and wonderful to ride, but I'm not sure the breed as a whole is the strongest for driving or jumping.
So, having mumbled through all of that, I guess I would vote for an Indian Shuffling Appy, a MFT, or a gaited Morgan. But I would really like to hear what others think.