I am a bit cautious about generalizing about various types of drivers and speakers; there are really good and bad implementations of all types. Given this caveat, I do agree that large coned woofers can be very fast and dynamic and deliver tone. I have heard terrific 18" drivers that can do this. They typically have light paper cones and pleated paper surrounds. Despite their size, they are not designed to go very deep in the bass range (the pleated paper surround restricts the range of fore and aft movement). But, properly implemented, they can deliver very tuneful bass. The high efficiency of many such drivers make them suitable for use with low-powered amps (my favorite kinds of amps).
The kind of dynamics the OP wants is less a function of deep bass than what the speaker can do in the midrange. When done right, horn/compression drivers are hard to beat in this department. They can sound extremely dynamic at surprisingly LOW volume. I actually prefer large horn systems playing at low volume than when they are cranked up very loud (they tend to "shout" at high volume. That might account for the popularity of huge horn systems in Japan where the size makes no obvious sense, given the small rooms. But, horns sound good in small rooms (my guess is their directivity reduces the influence of the side and back walls) and because they can be played at low volume, they would work in Japanese apartments.
I've also heard startlingly dynamic sounds at not crazy volume levels from some panel type speakers. I recently heard stacked Quad 57s with custom active crossovers to two custom tube amps at the Capital Audiofest deliver great dynamics. The Sanders Sound electrostatics I've heard were also extremely dynamic.