The four characteristics are:
Flexibility: how easy is it to alter the base tone. Very flexible pieces have tones that are easily bent and techniques like lip bends and squeeze tones become easier. The more flexible a piece is the harder it is to keep in tune, as a general rule of thumb.
Core Tone: This is a measure of how many harmonics are present in the base tone. Less core means more harmonics and thus a more "color" tone. Whereas more tone means the piece will blend better into ensembles.
Brightness: This is a measure of how prominent the high harmonics are in the tone. The brighter the tone the more it cuts through the ensemble and is considered more contemporary.
Volume: How loud is the piece? Can it be heard from space?