the precision bass comes equiped with the split single coil bass pick up, this was designed after the tele bass, the 50's precision (sting precision) to reduce hum from the single 4 pole pick up.
the jazz bass has 2 single coil pickups, one near the bridge and the other just a little towards where the neck joint starts.
simple, just use the neck pick up on the jazz and bear with hum from the lighting equitment when you play live or full on both pick ups and pluck/play over the space between the neck pick up and the neck joint.....full blown bottom...use the tone sparingly...