I think the differences in sound between the 10' series and the 12" series speaker cabs by Barefaced have been pretty thoroughly covered in this thread, though its long so probably easy to miss... 10's are more colored, vintage-y but they can do more than be vintage-y... 12's are more clear... BT2 has a horn so maybe you'd miss that, dunno... The 10's are also good, probably better, if you use tube amps or a distorted, overdriven tone.
I'd suggest that if you like the sound of the BT2, but want something small and easily portable for smaller gigs, consider a Super Midget... 21 pounds, 12" speaker, horn... small box, about the size of a small guitar amp (like a Fender Champ or something). There is no small gig it won't handle with aplomb, and many bigger gigs as well. I don't have the Two10 or the BT2 but I do have a SM and a BB2, which are similar in sound to the BT2, and a One10 and Four10, similar in sound to a Two10.