It's not unusual for there to be some variance in output -- with passive basses especially.
That said, a couple of considerations would be:
PU height: "physically as high as they will go" is not necessarily the spot that they are the hottest. You can get them too close and it actually makes it worse. There is always a "sweet spot" for a PU and you just have to experiment until you find it.
EQ: Jazz basses tend to be mid heavy. If you are EQing out some of the mids, you could be attenuating a great deal of the output.
Perception: If you are accustomed to the fuller, more rounded sound of a P bass, the less "bassy" jazz may sound thinner to you.
Of course, it is reasonable that it is just the way it is. That's why there's a gain trim on bass amps.
