No experience with the BBII. I have recently moved from a Super Compact and Midget setup and they were very good cabs. They are not magic, though, and a BBII or a SC alone will not replace a 2 x 112 setup. The cab I replaced my 2 with (Berg CN212) seems to be around the same kind of volume (perhaps a little louder, actually), but I would say the Berg 112 I had before the Barefaced setup was not quite as 'big' sounding as the SC. The build quality of the bergs feels somewhat better, for sure, if that kind of thing bothers you.
I wouldn't say there are any 2 way 1x12 cabs on the market that would be louder and deeper than a BBII on my experience with the SC, but again don't expect it to compete with a good 2x12 setup.