I've never had a Duncan Distortion, but I have experience with the Seymour Duncan JB.
I can say that the Miracle Man is a bit louder in output than the JB, and much more muscular and clearer. With heavy settings that really makes it stand apart, even if it doesn't sound much louder. The Nailbomb I felt is pretty much around the same output as the JB. You really get BKPs because of the increased frequency range and the transparency, but not for the output and compression; I've always felt that many Seymour Duncans get their sound from a fairly strong output level, maybe even unneccesarily loud, that comes from quite a lot of compression especially in the mid and bass frequencies. None of them seem to have the same mid and bass transparency from BKP.