I'm not convinced by the 'signature tone' thing. There is a fair difference between the tones of the BF Midget and Compact, and between the Compact and the Super 12. In a blindfold test I could tell you there was a difference, and could probably pick out the Midget, which kind of suggests there isn't a signature BF tone.
I've never walked into a gig or rehearsal room while a band was playing, and thought 'that's a [fill in the blank] cab' before seeing the rig.