So a squire Jazzbass? I mean it's almost the same, it's indeed single split pickup in the middle vs 2 pick ups neck & bridge.
J-bass is an iconic sound, the solo Jaco sound or you can go nice and warm and dubby with the neck pick up.
It has more sonic variety, but I find it a bit scooped against a P-bass which has a bit more push, you can just plug it in and put it under any track and you got bass within seconds.
If one plugs a J-bass in there's always this song and dance of finding the correct tone for the piece.
I've had a studio and it's definitely something I've observed many times, P-bass we're rolling! use an amp or not plug a di straight into the mixer and I've got a workable bass sound.
J-bass, oh here we go, 15 minutes of fiddling with the controls on the bass & amp, aah too bright & metallic, or hmm too deep & dark
Still a great instrument with its sound and its players, but for all round studio duty for most styles of music the P is a time saver