It is amazing how there are so many opinions among headphones with the same speakers inside.
The sound could only change if there is a baffle or other physical differences.
Troys, Koss and Ratphones have full range speakers.
A few points:
The volume control value will affect full volume and some tone. Only a little.
The limiter design may affect volume and some tone. (most have the same limiter design).
If the limiter is across the speaker, the volume control may get scratchy if the volume control is too low in watts.
Cup size is what you find comfortable.
The extra piece in the so called "louder" model only gives you a slight difference in very low frequency isolation.
Cord quality and length is very important.
Some cables resistors to be multi machine compatible. This cuts volume a little.
If full frequency phones sound bad on your machine, it is the machine.
Limited response speakers are very low in impedance in the lower frequencies. That is why there is no bass.
If you like just a screechy sound, you are not hearing everything.
I said, YOU ARE NOT HEARING EVERYTHING!

If you are talking to a crowd, you use a bullhorn. Limited response to pierce though.
If listening to sounds, that is different,