Maybe it will be a little off topic, but after hearing all the scientific stuff, I tried a Barefaced Big Baby II, and it sounded like a Mid/High P.A. cab. Very shy lows.
A Markbass Traveler 2x10, which is really not the fullest sounding cab, sounded like a bass stack next to it. So it was a very crappy experience, after reading all the great marketing propaganda stuff on tha Barefaced webpage. Embarrasing to read raving reviews as well about this cab...
This is very surprising. What amp were you using and did you try to change the EQ to get a similar response? My guess would be that the MB maybe has a hump in the response that made you think it sounds like it has more bass. I would expect that will a little EQ (and enough power) you could get much more bass from the BF than the MB. I've never tried that MB 2x10 though so this is just purely "spec"ulation on my part.