Which proves that it this has absolutely everything to do with the player, and absolutely nothing to do with the bass being used.
I don't know what P bass you're using, but mine has one tone. And by that I mean if you play the same note with your picking hand in the same position, and fiddle with the knobs, nothing really happens. The volume is pretty much off or on, and the tone control varies from "damn does that sound good" (about 0-3), and "woah... way too much treble." At least on my P bass... Of course, I make all sorts of different tones with my fingers. It's the rider, not the bicycle that wins the race.