I think a pedal is going to be a LOT easier to manage live. I'm just thinking of the nightmare of adjusting the output level on the fly if you are cranking the input gain of the preamp to overdrive it.
It's hard to describe - I actually don't have that much experience pushing tube preamps into distortion territory, though I do have a fair amount of experience with pedals. One thing to watch out for with pedals is that they might lose some of the lower frequencies, especially if they weren't designed with bass in mind. Even the Fulltone Bass Drive has a rep for losing a little low end, though I've never had a problem - a lot depends on the context, technique, etc. If it's a melodic solo then that might not matter, but if it's a bass line then losing the low end could suck!
There's also the issue of how much distortion you actually want, and the tonal character of said distortion. I got a Homebrew Electronics Hematoma bass distortion/clean boost - love the boost for solos, but the distortion was a little too mellow for me, so I've gone back to the Fulltone for now. Fuzz can be great but can also be a little too over the top? Also, fuzz often doesn't work with active basses - that's why I picked up the Z Vex Mastotron, because it is compatible.
I haven't heard the Marcus Miller song you mentioned so not sure what tonal character you might be after.