Originally Posted by BrandonBass
All things being equal, there is no reason why a P would be better than a PJ.
All things are seldom equal, however. A whole lot of PJ basses have the P pickup in the "wrong" spot. Small deviations may not vary a whole lot, depends on the listener's tastes, but a lot of them have it pretty far off. I think that among current Fenders only those built on Precision bodies have the P pickup in the right spot. The rest have it anywhere from a little off to significantly off. Other brands also vary a lot. A second problem is that PJ basses generally have a third pot and that changes the electrical loading on the P pickup and changes the tone a bit.
If you are careful to buy a PJ with the correct pickup placement and are willing to modify the electronics (if needed) to give you just two pots in the P only mode you can certainly get an authentic P sound out of a PJ. And then you also have more tonal range when you use the J pickup.