One thing that's not been mentioned yet, is that if you're looking to use a distortion/fuzz/overdrive on your bass, then you need to find one that is specifically for bass use, in other words, it has a "Blend"/"Mix" function on it,
Distortion etc. robs the bass of the low end, and so although it'll sound great on it's own, it'll get lost in a band situation. Which is where the "Blend"/"Mix" comes in. You need to keep a certain amount of the clean signal coming through in order to keep the low end. Start at 50% mix, & work from there.
Bearing that in mind, the BDI21 is the one to go for.