Regarding the difference in sound:

P-Bass: Blah blah blah

J-Bass: Nah Nah Nah

Music Man Stingray: Dah Dah Dah

This is the truth is stick by!

I've got both and a fretless Jazz....Use them to record and live...I use LaBella Black Nylon Tape Wound Bass Strings  and have since 1970.  This is the best of both worlds!
 
meh

I love both and mainly record with a Jazz bass, but P-Bass is sort of the gold standard of electric basses, especially for Rock and Pop.

Would you say use the Jazz if you want to hear the defined bass melodic lines and the P if you want rhythm and a foundation to work with the kik?

Depends on the PU... I put a Jazz bass PU on my P bass... 
There are more variations than there are bass players,, to say one is better or worse is talking through your backdoor porthole... 

Fair enough, in plank wood instruments like these, the PUPs and amps are the sound.
However, a modified guitar is hardly relevant to a discussion about the described instruments.
We have to assume he is discounting mods but, unless DI, an amp is certainly going to make a huge diff.

J

80% of the sound is touch and technique.  Ten different players can play the same bass and have ten different sounds.  I've always preferred the J...but both are great basses.

A buddy of mine swears by his Gibson Thunderbird...and he has two MM Stingrays and several other basses.

konradh

PS I have tried to record bass with an actual bass instead of samples; and playing bass cleanly is way harder than it looks if you don't do it every day. And being creative while keeping things simple is a huge challenge. I tip my hat to all you bassists.

Ha, love it!
 
I know the original question was regarding Fender options, but i'm yet to hear anything that my Musicman (Sterling) hasn't shined on. If you are spending some coin on a bass, go check one out.

Teds_Studio


80% of the sound is touch and technique.  Ten different players can play the same bass and have ten different sounds.  I've always preferred the J...but both are great basses.

A buddy of mine swears by his Gibson Thunderbird...and he has two MM Stingrays and several other basses.

No disrespect Ted, but IMO, 80% of the "sound" is still the machine. However, I agree that 80% (or more) of a great track is the performance. (The singer not the song). So to compare the J with the P, we have to have equal performances and equal amps.