Thanks ed a good question..
the efficiency of a given loud speaker is proportional to the square of the air gap magnet strength, which means that the doubling of the field strength will result in the doubling of the sound pressure produced by it
the efficeint speaker has a short voice coil travel, needs less power, and this mean less of a cone movement to produce more volume
i think because it moves faster it draws less current as there is less of a load
the less efficient speaker does the oposite of the above.. ie has a longer travel to produce less volume using more voltage to provide similar volumes.. so if the voice coil has to travel up to 5 x the distance to make the same note at the same volume, it will operate for longer and is more of current drain..
i am having an issue at work with a machine that operates on solenid valves ( which work nearly the same way as a speaker motor)
with load they are drawing more current, and the voltage is dropping as a result , causing them to slow in operation, depending on the load on them.
this could easily happen in speakers when up against large peaks in music
so i think that answers to your question