I've owned a number of PJs, starting with some hot-rod mods I did back in the late 70's, up to a 2010 Sadowsky. For me the biggest difference between PJ and JJ -- with both pickups on -- is on the D and G strings. With PJ, the E and A are Jazz-like, but the D and G are snappier... or thinner, depending on your POV. With reverse PJ, the difference is in the E and A strings: they are either growlier, or less thumpy, than JJ... but the D and G are more similar to JJ.
IMO, IME, and all that.
This makes perfect sense as the A & E coil is in the normal location of a neck position J pickup.
Roger