I think the reason both the Acme and Barefaced cabs are power hungry is that both are tuned low. Since the Acme is less efficient I figured that it's probably because of being tuned lower. I don't care about efficiency but do care about going as deep as possible with as little rolloff as possible.
Barefaced have not been called power hungry by anyone I know of, but it's a common description I've seen for Acme. My experience with the BB2 says it isn't power hungry. It also isn't tuned low, though it has plenty of low end extension for most players.
IME YMMV ETC