Efficiency of speakers?

There is not a direct connection between speaker sensitivity and transient response. That said, some speakers acheive high sensitivity by using massive magnet structures coupled with very light weight cones which should make them very quick sounding drivers. But again there is no direct connection the way you're implying.

I don't think that your question can be answered with the single variable of amp wattage. The speaker efficiency that you are referring to is a measure of sound pressure level. In other words, what is the output level of a speaker driven by 1 watt measured at a distance of 1 meter on axis. The transient response, or "quickness", of a speaker is something different. Bigger amps in terms of wattage will not necessarily give better transients. They may or they may not. For example, for dynamic speakers, cone movement must be well controlled or this will blur transients. If the larger wattage amp has better control of the cone, it will produce better transisents. If not, it won't. It depends on the amp's design, of which wattage is only one part. The speaker itself is also a variable. Electrostats, for example, are lighter than cones and typically have good transients because the lighter driver is easier to start and stop, even if the cone and electrostat have the same "efficiency", all other things equal of course. So I think that the answer to your question is "maybe". It depends on a bunch of other variables besides the sound pressure level measurement of a speaker.

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.