I have never owned a precision, and recently acquired a Jazz copy... But...Not really. I've got two P basses and I think that any well built bass, with good strings and a great player will record great.
After 40+ years of playing and about 50 records and thousands of gigs... If I needed a go to bass for gigs and
session work going on MY experience...
Precision... Period.
Gary Moore told me he needed me to play it in order for him to get "his" sound. There are variations on good
tone whether Alembic, Stingray, Jazz, Ripper, Grabber, etc., but the PBass is a standard safe bet. Don't forget Patrice Rushen's "forget me nots"... Slapped PBAss...
If you've got a Stingray, a Jazz, and a Precision, you've got everything covered, one way or another... In regards to live/studio. I've always wanted one, but getting a good one isn't hard, but an exceptional one is... IMO...