I'mm a distortion/overdrive junky. I'm on a seeming endless quest to find the perfect distortion. I've had different rigs, diifferent cabs, different stomp boxes. and different basses. i never get rid of distortion pedals. becuase i feel like one day, i might want waht that pedal gives me in a tone. or, some day i might own a rig that doesn't sound right with the pedal i was using at the time and need to switch.
early on i was looking a tone similiar to my favorite bassist, RObert Wynia of Floater. it always sounded like there were two signals, a very clear and defined low end tone, but tracking just a hair behind it was this miraculously fuzz.
It drove me insane that couldn't duplicate it, and hundreds on hundreds of dollars have been spent searching for the answer.
turns out, as i learned in a conversation with Rob a few years later, he missed his original distortion tone becuase he bought the new model of the boss multi effect board he used to create it. despite it being the same "model" it was an update and did not produce the same distortion.
what i learned from this conversation is that he wasn't just using a distortion, but instead he had carefully(?) crafted this tone from a combination of distortion, chorus, and various other effects.
My point here is, you might be chasing a distortion tone that may be a result of multiple layers of effects and tracking.
Now here is some information that is closer to the answer of your question. I own all these pedals.
Ibanez Tube screamer- great sounding distortion that really pulls some serious upper mid "growl". but it still sucks alittle of your low end out. I recommend you put it either in line between your bass and your amp, allowing your pre amp to compensate for the low end loss, or if you have a seperate preamp ( like a sansamp,) or an equilizer pedal (like the boss bass equilizer) you can put the the pedal in your effects loop as long as you have it before one of those. Also, a chorus pedal, or an octave pedal after the screamer in the chain might give some lower heavier tones.
Boss ODB-3 Bass OVerdrive; I was never happy with this pedal. no matter how i set it up, it always seemed really muddy to me. the only tone i was ever able to get was a tone similiar to Cliff burton's on pulling teeth. but I could get that out of other pedals as well. it's possible that it maysound better with a different rig, at the time i was pushing it through an svt-4PRO with an 8-10. I use a TC Electronic RH450 now through a TC RS212 and a SWR (prefender) goliath 3 410 now, so it's it's entirely possible that it might sound good with that rig.
(The TC head has a rediculously nice Tube emulator that is circuited through bot th the pre amp and the power amp, so it performs just like a real tube amp. (it goes to 12!) so i really don't use much in the way of external overdrive anymore)
MXR zakk wylde overdrive- yes i know this is a guitar pedal, not a bass pedal, but it was a gift. and if you want to take something to a rediculous level, this can actually be really sick. not gonna bother telling you about it in depth though, you really should spend your money on something useful.
DIGITECH BP80- entry level multi-effects pedal for bass. It's good for playing around until you really know what you like effects wise. occasionally i still pull it out for some experimentation. there are some good distortion tones onthis, it has a three band EQ so you can boost any low end loss. also, a drum machine and metronome. not a fan of it's wah effects though. There are better multi effects pedals out there, but this one is cheap and sounds decent.
EBS VALVE DRIVER- so far, this is my favorite pedal overdrive for bass. It's tube driven with a 12ax7 providing warmth and some serious crunch. three band EQ, gain and volume make this thing jsut evil. it has two foot switches. one is a circuit swtich from a "modern" tone to a "vintage tone" the other is a bypass/mute switch. (there is a small button onthe back to change the function of this foot switch) No battery power for this beasty, and you have to use the included power cable becuase it operates on a different voltage than most generic power strings. But it is seriously a powerhouse of tone.
and then my one other kind of overdrive i've owned is the on board tube emulation on my TC RH450. it goes from 0 to 12, and is absolutely insane. you get everything from a soft, barely noticable warmth, to a scrunched, crunched and crackling overdrive. it's routed through both the preamp and power section so as you turn up the volume, your drive becomes tastier and tastier. i've gotten some unbeleivablely awesome tone from this head. check it out. i dare yah.
so, have fun, good luck !!