It's hard to say that these boxes sound like this or like that, because as with any good DI, both units do their job well and don't sound like anything at all. With my Fender Marcus Miller Signature Jazz Bass, which features both active and passive pickups, both units handled the signal well. I really like the sound of that instrument's active circuit, so here the SB-2 was the better choice.
At my usual live sound gig, the SB-2 was a huge step up in sound and build from the usual cheap fare. It was also nice to have the active SB-1 for bass, since one of our usual bass players uses a Danelectro model which is is known for its unique vintage sound, but has notoriously low output. Smiles all around, which is what an engineer wants to see.