For reference:
http://youtube.com/watch?v=GUkiFLURt38
Pretty much
all we talk about in this forum is how to get the tone of an aggro bass through a cranked SVT by buying a small, inexpensive pedal.

I'm exaggerating, but not by all that much.
For starters there is the whole Sansamp line, which are designed to emulate the SVT sound. Then there are about four or five hundred decent-to-good overdrive and distortion pedals. Then there are a few "holy grail" pedals that step up above the rest, but they are invariably expensive and hard to find. The main one to read up on IMO is the BJFE Blueberry. In the more accessible category are the "boutique" clones of the old Ibanez Tubescreamer, such as the Fulltone Bassdrive, Xotic BB, and practically every other boutique pedal that calls itself a bass overdrive.
Anyway, pedals are great and often do the job just fine, but it's very very subjective. No pedal sounds
identical to a cranked SVT, so if that's the tone you're after it's all about finding a compromise that will do the job well enough for your purposes.
In that video there is distortion on the chorus, but it's really hard to tell if any of that distortion is coming from the bass, or if it's just the guitars overlapping those frequencies. The only time I was
sure I heard the bass distorting was in the last seconds of the track.