The Hunter Derby, if you are talking about the new USHJA International Hunter Derby's, differ basically in fence construction and the track of the course.
The fences are supposed to resemble the types of fences you would see in an actual Hunt field.
The courses are supposed to be a departure from the modern Hunter courses, which are basically comprised of outside lines and diagonals lines only.
The International Hunter Derby's were created by the USHJA with some lofty ideals of returning Hunters to their roots, generating enough interest to turn it into an international competition, as opposed to the North American discipline it has been, and to create spectator interest and ultimately sponsorship, which should theoretically bolster its international competition legitimacy.
Plus they added a bunch of prize money, and finals to get the ball rolling.
Not sure if its working, seems to me it is the same old horses competing, with the same ole' riders, jumping a different course the same ole' way. The fences are nicer, but I think until they start putting the majority of these classes out in a grass field, with natural elements, and jacking the fences up to at least 4'3", and the riders really start to hunt around these course it is just a glossy version of a modern Hunter class.