I've tried lots of P's over the years and the only two I really get along with are Peaveys and Japanese Fenders which seem to have a slim front to back neck profile and are relatively narrow.
If you're in the same world I am (some gigs almost require the name fender on the front and california on the back... there were some pbass specials that had a neck almost identical to a fury. Sucks to then have to make it look and sound better.. but I'm not going to change perception.
....... consensus is on the USA Millenniums Peavey did awhile back. ......
This is a preference thing.... for some reason they weren't big demand when they were released.
For some reason, when properly setup, they fit my perception and feel the best. When my house was on fire, I bypassed all of the botiques and collectables and brought one single Millenium (I own 2).
Stock the setup is not that great... once they're dialed in, they are just about as perfect as it gets.
LINKS
Recording
This recording is direct to the board (only a cable between)
I put this in as there are some hits that will show what they sound isolated and in a band context.
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Live
This one has a GK plex in between the bass and mains
I put this in as it indicates how bombastic they can be setup to be.... sorry of the flubs, we recorded this in a zero light room (live)
Hope this helps