True, but what is the tradeoff? If there were none, I would imagine they would build high-efficienty speakers (unless they also sold high powered amps) :) No?
The problem with high efficiency speakers is that the drivers cost about 10 times more than lower efficiency drivers, for the most part.
Otherwise, in general, the more efficiency, the more likely that bass extension will be compromised. Most speakers over 102 db or so do not go below 40-50Hz. However they are capable of all the resolution and musicality of speakers of lessor efficiency, if constructed properly.
My speakers (Classic Audio Loudspeakers) trade off efficiency for extended bass. They go to 20Hz but are only 98 db. However they are as revealing as any I have heard.