The question is a good one and deserves a straight forward answer. Five steps should be taken in testing a mouthpiece:
(1) Use several reeds of slightly different strengths. Your favorite reed is probably comfortable on your current mouthpiece.
(2) Be certain that the reed is placed correctly on the mouthpiece, that its tip is even with the mouthpiece tip, and that it is centered from side to side.
(3) Does the reed seal? Keeping the end covered, draw the air out of it and then take the mouthpiece from your mouth. A popping sound means that the reed is fitting properly on the mouthpiece. A warped reed will not pop because air is escaping between it and the mouthpiece.
(4) Tune to 3rd line B natural on alto, tenor, or baritone saxophone (5th line F sharp on soprano) to its respective concert pitch. This note may be tuned slightly flat but never sharp. Improper mouthpiece position can cause bad intonation, poor response, and inferior tone quality.
(5) Do some playing in all registers, from lyrical to rapid staccato, using various dynamic levels. Repeat the examples several times. Then play them, using your own reed and mouthpiece. Now try the new mouthpiece and reed again.
Many players like to record this test, which allows them to "stand back and listen." Some prefer to have one or more musician-friends listen as each mouthpiece is played. If you use these "judges," be sure that they cannot see which mouthpiece is being played. Listen with your ears, not with your eyes. Be patient. Mouthpiece testing takes time. Finally, how does the new mouthpiece feel to you? To make the right decision you must like the way it sounds and the way it feels.