Take the P as the yardstick, then the J has the following:
Thinner neck
More pick ups
Pickups in different locations under the strings (harmonics and vibrations-stuff differences)
More knobs
Same length of neck usually
May have different woods in the body and/or neck
Brighter, cleaner sound, but less punch in the mix
Buy a MIM since they both have MIA pickups, necks made in Corona (USA) and the electronics are really the same.
Rats! Now I'll get the Fender knee breakers at my door again for letting that secret out.
I also feel that you cannot be complete without one of each - a J and a P. But beware! The Squiers are fast becoming the better one in price, tone and looks.
The MIAs and some of the MIMs are getting rather higher priced than they should really be in this economy I feel.
Of course - also the above (^) is somewhat anecdotal and is a combination of MY results.
These are my anecdotes anyway.