Very different.
Nothing sounds like a J Bass with both pickups turned up, its got a really nice scooped out mid range, best slap sound you can get IMO. but when soling the neck pickup, it wont sound like P Bass.
The advantage of the PJ is that you can have a proper P bass tone when soloing the neck pick up and or a proper J Bass (Jaco) tone from the bridge pick up. When they are both up together it sounds nice but it wont sound like JJ.
I find PJ more versatile. although i love the J Bass sound jaming on my own, when playing in the band setting the P just cuts through the mix better.