My first two basses were P clones, I never liked the tone. Then my third bass, a Pedulla Series II had a PJ set up and I only liked the sound with both pick ups or just the bridge pick up on. I'm not a big fan of the P tone, turns out I never was.
That's it right there. If you love classic P-bass tone (like I do) you've got to have a Precision (or two). But if that's not your tone, no reason to own one. (And if a studio producer insists on your using one, borrow one from a friend.)

