I think that's really down to the amp's EQ. I like a quite thumping bottom end, but I was rehearsing yesterday and the band felt it was too boomy (I was using the rehearsal studio's amp and cabs) so I wound down the bass on the amp and boosted the upper mids, it then had bite to spare. And that was the LaBella equipped Precision, played with fingers. In fact, for my taste, it was too toppy, so I'll take my own amp and cab next time.
So even a 'bassy bass' like a Precision with LaBellas on it can be made trebly. I think the LBs excel at producing a warm mid range that sits well in a live situation. Yesterday's band was a 6 piece, with two guitarists, keys and 2 drummers in addition to my bass.