I'd have to say that the setup, technique and some overdrive have more to do with the tone in those videos than the bass its self.
Fender Jazz basses have a particular tone, so you'd want to start there. I think really just about any would do. A lot of the "growl" there is actually a result of low action, very little relief in the neck, and the pickups being pretty close to the strings. I also noticed that the players are digging in pretty forcefully on the bridge pickup. Some nickle round wound strings should finish the instrument part of it.
I'll bet good money that there is a dirt pedal being used in all of those videos. A Sansamp BDDI sounds about right or VT Bass. Personally I use a Pork Loin for dirt, but I don't think you'll get those kind of present highs out of that pedal.
For my tastes I wouldn't call that tone growl as much as I would bark or grit. When I hear the word growl I think more of those hi-low/lo-mid freqs that add real character to the low end of a bass. The audible, recording friendly, lows that come at you like a panther about to tear your face off.