It's a little hard to put into words, but here goes - this refers to a MIJ re-issue with the mustang pickup, and the P pickup on the P/J Mustang.
The MIJ sounds to me a bit thumpier, with a more restricted range of frequencies, and not as 'hi-fi' sounding as the P on the P/J.
This is just from me listening quite closely to them for a while. Same amp, same strings, same settings, except for the volume.
I have to nudge the volume up just a tinch on the MIJ to equal the output of the P/J.
I'm sure the average listener wouldn't hear any difference at all.
And I think even most bass players would probably say the difference is not enough to sway their choice either way.
So, it's definitely a case of YMMV.