What are the differences between fender Precision bass or Fender Jazz bass?

The main differences are:

P-Bass has slightly wider neck, Jazz slightly narrower.
P-Bass has one pickup, Jazz has two.

The pickups sound different, but I’m not a bass aficionado. I’ve seen guys play both for all types of music (which is to say the Jazz Bass isn’t just for Jazz). Fender also makes P-Bass “Specials” which is an instrument with the narrower neck and two pickups—one being the standard split P-bass pickup, the other a standard Jazz pickup. My two cents would be to get the P-Bass, but the ultimate decision will come from playing both.

I just got a P-Bass 60th Anniversary Edition and I love it. It’s got a Badass bridge that holds the notes forever. While I’ve not compared a P-Bass and Jazz bass side by side, my impression is that the P-Bass has a thumpier, gut-moving sound while the Jazz bass is more mellow and round.

If you’re torn between the two, go for the P-Bass Special. It’s a nice hybrid between the two, and is one of the more versatile basses I’ve ever played, good for any type of music. It’s also fairly affordable.

If you’re not torn on either a P-Bass or a J-Bass, you will want to take a good long look at the Jaguar. It’s got Jazz Bass pickups, but also some huge tonal capabilities via pickup coiltapping, pickup switching, and pickup specific volume and tone controls. Put it simply, you can get any tone out of it you want. It’s also competitively priced.