You cannot compare efficiency alone without considering speaker/cone size and overall design...it is always a compromise.
The question:
If driven with the appropriate amplifier(s), meaning a higher powered amplifier for a less efficient speaker and a lower powered amplifier for a more efficent speaker, are there any difference?
The speaker design is generally what makes the difference.
An inefficient bookshelf speaker with a big amplifier can be comparable to a full size efficient speaker with a small amplifier when played at acceptable sound levels for both the bookshelf speaker and small amp.
A bigger speaker can ultimately go louder with less distortion particularly when pared with a big amplifier.
On the other hand,
An efficient bookshelf speaker, is rarely comparable to a full size efficient speaker.(Bookshelf being roughly up to 6" woofers, and full size being 12" or larger woofers)
In very general terms:
1) big speakers can be efficient, and play loudest with lowest distortion
2) small speakers tend to be inefficient if they have low distortion.
3) efficient small speakers tend to have the highest distortion even if they can play quite loud with a modest amplifier.