I was under the impression that speaker efficiency is not the same as speaker sensitivity. Speakers are quite inefficient, in that most of the work done by the amplifier is lost as heat.
More efficient speakers generally have larger cabinets. Many speakers nowadays are not designed for efficiency and try to produce an 'uncoloured sound'. This is to fit in with demand for smaller, less obtrusive speaker designs. The problem is that inefficient designs, while able to produce such uncoloured sound, can lack the range and loudness to reproduce music faithfully. Inefficient designs presumably make greater demands on the amplifier, though I am not sure as to the importance of this point.
I think I am correct in thinking of sensitivity versus efficiency like this, that if two speakers have the same sensitivity, one might be more efficient, in that for the same electrical work, you get greater bass response.