I'm of the mindset that wood adds to the overall tone but it's not JUST the body wood. It's the combination (neck wood, fingerboard wood, pickups, pickup placement, construction, strings, set-up, technique, player's fingers). I really don't think body wood alone makes a huge difference.
I think "growl" comes more from the pickups/electronics, strings and player technique. Geddy Lee gets some nice growl out of a Jazz Bass, probably due to his very aggressive fingering technique.
I started playing bass with a pick (originally a guitarist) then switched to thumb, but have recently been playing more with thumb/index/middle finger. I've noticed that my index finger is kind of flat at the tip so when I play I get a sort of clank from my fingernail and an overall brighter, slightly more aggressive tone. I've cut my fingernails as short as I can and it still happens. Annoying since I like a more rounded tone (I also play over the neck pickup).
But it's amazing the difference in tone just from index finger to middle finger due to my weird anatomy, lol.