The only issue is cosmetic . A p bass looks best as a P and not with that dirty little J creeping up on it . 
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Nice!
Resistance for a typical, vintage-y split P is often in the 10-12.5K zone, a single coil J in the 6.5-8K range.
This is just resistance of the coil, which is not directly tied to output, which includes inductance and magnet strength to the equation. A lower wind coil (lower resistance) with strong magnets can have more output than a hot wound coil with weak magnets.
I find many inexpensive import instruments that have a humbucker to use 500K pots all around. It's probably to keep it simple for production and offset the loading from having multiple pots. 250K is Fender standard and the P and Js. I like to use a 500K tone pot with 250K volumes, it just gives a touch more range to dial in the 'air' to the tone. Once turned back to around 7-8, it sounds just like a 250K tone pot on 10. My P/J has a 500K tone and volume and a 250K M/N blend.
I was just talking about using an amp to change a P bass's output within it's already excellent tone parameters. Geeeez, why would anyone even want a good P bass to sound like something it isn't? -Or, for that matter, a Mustang? Is a PJ Mustang a real Mustang or just something patched together by Fender to cash in on what's 'trendy?? Hey, if someone really likes the odd extra tones one can get from a PJ, that's fine. That's one thing... But don't try to tell me it's an 'improvement' over a P or a Mustang!EQ controls on an amp cannot replicate the complex, phase induced comb filtering from having two pickups (let alone two different styles of pickups) interacting on different harmonic zones of the string.
Perhaps a very detailed and deep EQ session on a DAW might get a P to sound sort-of like a P/J with both pickups blended.
I was just talking about using an amp to change a P bass's output within it's already excellent tone parameters. Geeeez, why would anyone even want a good P bass to sound like something it isn't? -Or, for that matter, a Mustang? Is a PJ Mustang a real Mustang or just something patched together by Fender to cash in on what's 'trendy?? Hey, if someone really likes the odd extra tones one can get from a PJ, that's fine. That's one thing... But don't try to tell me it's an 'improvement' over a P or a Mustang!
I was just talking about using an amp to change a P bass's output within it's already excellent tone parameters. Geeeez, why would anyone even want a good P bass to sound like something it isn't? -Or, for that matter, a Mustang? Is a PJ Mustang a real Mustang or just something patched together by Fender to cash in on what's 'trendy?? Hey, if someone really likes the odd extra tones one can get from a PJ, that's fine. That's one thing... But don't try to tell me it's an 'improvement' over a P or a Mustang!
OK, sounds reasonable... There's room for everyone's likes and dislikes in the bass world I guess. I'm not really anti-PJ for anyone else just because I don't like them...Haven't really seen anyone say it's a flat out improvement, but if I need a slap tone for a few songs, having the J gives me that, which makes it an improvement for me.
IMO a PJ is a P with slight differences. I own 2 and they are first and foremost a P and second a P+.
If anyone wants any part of the sound of a J bass, get a J. That's what I did. It's the best bass for that.
YMMV
What is that??