My opinion - for what it's worth - echoes what most of you are saying. They're both great, but preferences is preferences. I've tried endlessly to love jazz basses. Lots of my heroes played them. There are WAY more options available in JB's to us leftys than there are in PB's. But no matter how much I try, I just can't dial in a tone for the kinda rock and roll I need to play on a JB the way I can on a PB. Plus, I'm not a fan of the skinny JB necks and can never seem to get comfortable with where to put my left hand on a JB. Everything falls right into place with a PB for me.
My band, over 20 years and 7 records, has been pretty diverse in it's palette. We range from boogie, to prog, to punk, to mild stoner tendencies. I settled in on PJ equipped basses a few years ago and like a previous post mentioned, couldn't get the balance between the pickups I wanted. Then I tried the EMG passive Geezer Butler P/Us (I know, I know, I've raved about these before...). These have WAY more balance and a great late sixties tone... but louder. If I want that PB thump I just turn off the J P/U completely. If I want more articulation, I run them both full out or just favour the P P/U slightly. If I want some tight growl, I will favour the J P/U slightly. I just ordered a new fancy P body from Warmoth with a PJ rout so I can rebuild my 8 string to have the same P/U config as my go to PB.
I'll always have a Jazz bass or two in my collection. But they will never get the love from me that my P basses get. My hands and my style just don't make them sound nearly as good. And that ain't no myth.