An American Deluxe Precision has been my main axe for 12 yesrs. It has one of the best, low-action necks I've ever played which can be set up with smooth, low, no-buzz action. Great fit and finish on the neck, fingerboard (rosewood) and frets.
It gets the classic P-tones in spades. I have a passive P-bass (USA) as well, which is also a great bass; but it doesn't quite have the neck action of the FADP (though it's close).
IME, however, the FADP does
not precisely replicate the classic Jazz bass sounds I sometimes want. The humbucker is extremely versatile, mixes very well with the P-pickup and enables the bass to get a super vatriety of usable tones. To my ears, however, it doesn't quite get the classic bark and bite of the J-bass bridge pick-up or the under-heralded deepest lows of the J-bass neck pickup or neck & bridge pickups together. A a result, I own a Jazz (USA), too, for those tones.
Though the FADP and the passive P have very similar, classic P-tones, I've been consideriing adding an active/passive push/pull control knob. The passive P has a few tones I like slightly better than the FADP with cetain amplication rigs on a few songs, but I'm really splitting hairs on this issue. I'm sure I'm the only member of my band who can tell the difference. It also gives me the passive backup option if a battery dies during a gig. To be honest, however, I change the 9V, high-qaulity alkaline battery once a year and have never had a dead battery problem.
All in all, the FADP is the best-playing, most versatile sounding bass I've found (though I'm always searching for the perfect P/J and would like to try a Stu Hamm Urge on a gig). It's my meat-and-potatoes AND gravy. Everything else is just a slightly different kind of gravy.
Bluesy Soul
P. S. BTW, I have tried the Sadowsky P/J (I posted a review somewhere here on TB last year). Though I find the Sadowsky produces excellent P-tones--and better classic Jazz tones than the FADP, I prefer the classic P-tones of the USA Fenders. (They are more vintage and old school to me, while the Sadowsky is a little more modern.) The big factor for me is the neck. The Sadowsky P/J comes with a J-bass neck geometry which is just too small for my hand (my Fender USA Jazz is a 5-string).