Efficiency of speakers?

Transient response is best with highly controlled woofers. Big Magnets. Short coil long gap. So that woofer is always fully controlled by the amplifier (large linear operating range ). The combination of woofer and suspension should be critically damped so after power signal stops it goes to zero without overshoot. This is what yields accurate transeint response - the woofer most closely follows the input signal...no extra oscillations.

This is not strictly related to efficiency and given the specifications you cannot draw a conclusion. However critically damped designs tend to be less efficient (unless they have huge magnets and huge boxes). Another factor that complicates things is a reflex port ...this changes a speaker to an infinite baffle below the port frequency and it will usually become totally under-damped below the port frequency and flop around.

My experience has been the opposite.
I have always found that less efficient speakers sound more controlled and have the capability to produce a more convincing sense of scale and dynamics. A good sealed box enclosure (infinite baffle) tends to be very inefficient, but if driven with sufficiently high quality power the result can be extremely accurate compared to all but the best ported designs. Many of the high efficiency speakers I have heard sounded relatively out of control to me.

Thanks all,I should have clarified that I am only interested in loudspeakers using conventional cones, regardless of their material, such as the Salon & WP8 as examples.

Because you're interested in cone speakers only, my experiences are only half usefull to you since I own a hybrid cone/ribbon design. Efficiency is low, due to the closed housing for the woofer and the low efficiency of the ribbon. The low-end is among the fastest and best controlled I've ever encountered. At first you think there's hardly any low-end, but baby, there sure is. So my experience suggests that the lower the efficiency, the faster the sound is.