I think P basses in general tend to have a weak B string. My theory is that the pole pieces allow the slowly oscillating, greater amplitude, lower tension B string be picked up less closer to the neck than other strings. When you have the pickup moved further to the bridge, like a MusicMan, it pickups up all of the wave of the B string. Additionally it has a single large pole piece.
There likely is something to this. I have some experience with Sadowsky P/J, and found the B string tightened up when dialing some of the J pickup into the blend. Still not a good as the Sadowsky "Modern," which places two soapbars down towards the bridge, sort of like the G&L L-2000. Wondering if the "bar" magnet in the Carvin split-coil might also improve on the single pole-piece Fender original.