I highly prefer the Super Distortion. It cuts significantly better and has more of an edge. It has lower output to my ear, so it works better with a wider variety of amps (i.e. with lower headroom amps). The JB has such strong output that it really likes to have an amp with plenty of headroom in order to keep the tone defined. If not, the JB gets real muddy real easy. For my amps, which are mostly low headroom amps, the Super D is a superior pickup. When I am considering buying a guitar, and it comes with a JB, I know it will have to go A.S.A.P. When considering buying a guitar, and it comes with Super Ds, I know that I might actually keep the stock pickups.
Another thing: The Super D works great in the neck position too. I can only imagine how awful a JB would be there.
The JB is great as a split pickup, though. It's the only thing I like about it.