I typically don't do this, but 'tis the season of giving
Tweak EQ to taste/room
Cheers!
I dig a lot the BB preamp too.
The drive is very nice and effective (I love the way it sounds on the highs : it adds a lot of presence) and according to the way you set gain you can achieve many different tones.
We may have similar sounds

(except that I prefer lighter picks. Doesn't sound as fat as the thick ones, but more soft for the hand when I play fast tunes)
I just prefered to put back my VT bass instead of the SVT model because I couldn't find the perfect way to match the sim cab and my amp.
Without cab sim : too much high end (no roll off of the highs). With it I can't dial well with the midscoop. But it's due mainly to the fact that I plug my B3 in a bass amp with a bass speaker, so not to a system with a flat response.
And the VT, that I set with a very light drive, cuts the trebles above 5 kHZ (kind of speaker sim, but without big dip in the mids) -> the BB sounds awesome.
I am making some tries with the Tube Screamer because I think it's capable of great tones, but I still have problems to keep a good low end with it and to reduce in the good way the boost in the mids (on its own I find it sounding very very honky).
Anyway, I made 3 patches with different levels of gain on the BB preamp, coupled to the parametric to manage the low lows cut if the room needs it + the Booster.
Like that I can cover my main needs, and I'm happy : big big sound !!!
I was so happy with my tone that yesterday I closed my eyes while we were playing (just to listen) and almost fell because my feet get trapped in the cables lying on the floor
