To me, the BFD sounded like a fuzz face. It's a less scooped and softer sound than a Big Muff. Frankly, I much prefered the MXR Bass Distortion, which is a Fuzzrocious modded RAT.
If I was after a Muff, it would be a front modded swollen pickle or a green Russian...but if I was after a rat...it would be the MXR Bass Distortion all day. For an overdrive....well that's a very different and tricky question to answer....
I don't find that my bfd gets lost in the mix at all.
The way I'm using mine leaves me with more low end girth and heft, and sits really nicely running through my Marshall rig.
However, I find that it doesn't work so nicely running into my hartke head