Dynamics, clarity, compression, distortion, all are interrelated and speaker efficiency, amplifier power, amplifier linearity, and more all enter into the equation.
All audio reproduction devices are essentially non-linear and become more non-linear as their physical and electrical limits are approached. If you plot the input vs: output of almost any device, the plot is not the diagonal straight line you would hope for, but is an "S" curve, with the curve flattening out the most as limits are approached. Thus one wants to run any audio device as far within its limits as possible as that is where the best linearity exists.
Speakers become non-linear as they near the mechanical limits of their suspensions. Amplifiers become non-linear as they approach their power supply rail limits, and even your ears become non-linear as they shut down to protect yourself from very loud noises.
Thus a reasonably good approach would be to have a relatively efficient speaker with good power handling capability driven by a very good amplifier with more than adequate power for it, fused to avoid accidental damage.
In general, horn loaded speakers, while gaining great efficiency, do this by trading off one form of non-linearity for another. The efficiency is gained by creating an acoustic amplifier, which is done by generating an underdamped resonant peak in the range the horn is tuned to. The problem with this approach is that underdamped resonators resonate, generating output by responding to harmonics of the tuned frequency, and with a frequency response that falls off very rapidly outside of the tuned horns range. A good "worse case" example is the honking sound of a cheerleaders megaphone. Of course a very low powered amplifier matched with a horn loaded loudspeaker may sound better than that same amplifier running at very high distortion trying to drive a less efficient speaker.
So as your system starts to compress, it is because the speakers, the amplifier, the room, or even your ears might be reaching their linear limits.
The real task is to carefully figure out which part is the worse case problem and fix that first.
Frank Van Alstine