The Honey Bee is reported to be designed to sound like a cranked Supro amp. I've never played a Supro so that doesn't mean anything to me
. That said, the HB is what many call a light overdrive, meaning that even with the drive cranked, it's not going to get as dirty as a normal overdrive. The HB, in general, has a unique sound. Whereas most of the overdrive world is comprised of Tubescreamer variations, the HB charts new territory I think. The Nature control on it changes how it sounds pretty dramatically. Also, I think as you play louder, the HB shines all the more. Lots of people seem to like it for various applications, but especially Americana / roots rock type stuff.
The BBOD is kind of the one that started it all in some respects. It's hard to put it in words, but the BBOD is still the king of the hill IMO. At every conceivable setting, you get pure (and useful) magic. It is more like a Tubescreamer than a Honeybee, but it is not a Tubescreamer, perhaps a distant cousin, twice removed or something like that. Versus the HB, the BBOD has much more hair on it's chest. It's a phenominal pedal for blues, but is equally awesome for rock n roll. Very versatile.
Hope that helps. I would put both of them on the must have list.