Well, I can tell you that it's NOT Parelli.
NH is just the newfangled 'cool' name for what boils down to common sense horse training. Which has been around for centuries; it just didn't have a name, circus atmosphere, or expensive, useless gadgets associated with it.
Classical training is the exact same thing as 'natural horsemanship', but without all the flash, trash, or smoke and mirrors.
You can ignore the ridiculous parts of NH, especially the expensive gear and the 'horsenality profile' garbage.