Danny seems to prefer the BB3000 and while they both sound good in the video, the difference in tone really isn't that apparent. Where the tonal difference really shines through, is when both are played side by side.
The rear pickup on both sounds identical - same blade pickup. The P pickup on the BB3000 sounds a lot like your typical Precision, though mid frequency is in a slightly different slot. However, with both pickups balanced, the BB3000 exhibits the same nasal tone that most trad PJs have because D and G pole pieces are so close to the bridge pickup and comb filtering of certain frequencies occurs as a result. This is not a tone I enjoy, especially when string popping, though it is less noticeable when playing fingerstyle. The reverse P on the BB2000 IMO sounds much more growly/throatier and warmer than the P on the BB3000, but where the BB2000 really shines though, is with both pickups balanced. The tone is much sweeter, and this immediately becomes apparent in the mix. Also, the slap tone on the BB2000 is without peer IMHO (even better than a Musicman stingray).
I bought my BB3000 on the pretext that being the next iteration of BB, it must therefore have been an improvement over the BB2000. Well, it's a little more ergonomic and a bit lighter, but for me, that's about it, whereas the neck on the BB2000 is perfect, and the tone is superb. Yes, it's a little larger and heavier than the BB3000, but those are minor issues. If ergonomics/slim neck width are your #1 criterion, then get a BB3000. If it's tone, get a BB2000. Tonally the BB3000 is really just like a better P bass with a bridge pickup, but the BB2000 is much more its own thing. Like a very smooth, yet very ballsy, souped-up jazz bass.