There is no blanket answer for this question. I studied with two very good women who helped me tremendously when I was young. Here are somethings to understand when trying to answer these questions for yourself:
-Muscular differences: There are two muscle groups in the larynx that help regulate the pitch and strength of the sound - The Thyroarytenoid (associated with Chest Voice) and the Cricothyroid (associated with Head Voice). A singer must coordinate the interaction of these two muscles in the correct way in order to make the desired sound without hurting themselves. A few examples: If a belter does not engage their true chest voice, they are more likely to squeeze muscles that should not be squeezed and end up hurting themselves when trying to make their head voice or mix sound belty. If a male singer wants to sing higher rock musicals and they train the chest voice too much, they will have a very powerful sound but likely no easy rock high notes because the head voice muscle is not strong enough to pull the vocal folds longer and thinner against the opposite pull of the chest voice. If a male singers spends too much time in a lighter head dominant sound (which many female opera singers use) they may end up sounding weak, nasal, and have difficulty staying on pitch. If a female wants to sing legit and carries up too much chest too high, they will often have a hard time getting the air out of their voice. However, if they have a lot of air in their voice on the top, it is often because they have no chest voice in the sound. A good teacher will balance both registers in all voice types so that the singer has the control necessary to sing throughout their range with strength, beauty, and finesse.
-Mimicking Sounds: Some students learn by imitation more than sensation or visual tools. For those singers, having a similarly voice teacher can make a big difference.
-Sensations vary not only by person but also by gender: I am married to a singer so I have a good idea of sensations that are different for women than men. If a teacher is not aware of those differences, it can be problematic.
-Repertoire: A teacher needs to have an understanding of repertoire for all voice types they teach and if they are not sure, they should be learning new repertoire as new students come to them.
-Breath Control: Lung Size, Subglottal pressure (the pressure of the upward air flow underneath the vocal folds), and vocal register are all tightly inter-related. Men and belters must breathe differently in the lower part of their voice than women and tenors in the top. The upper part of a baritone's range uses a different registration mix than a tenor's upper part and also in many cases requires a different approach to breath. Women approach their head voice (the high notes) much differently than men and their breathing strategy is often not beneficial to men (and vice versa). However, all of this can depend on the size of the singer's lungs and the strength of their abdominal wall (are they flabby or do they have a six pack). Classical singing requires a different resonance strategy than musical theatre which also affects the breath. Classical singers do not use microphones while musical theatre and pop/rock singers do. Because of this, classical singers need more breath and musical theatre singers (when not singing Golden Age rep) need less.
I think your best guide is your ears. Look up other students on YouTube of the same age, your son should be in the running with the others. There are freshmen showcase videos on YouTube, watch them because they are representative of your son's competition. You should expect that your son progresses each month (if he's practicing, if he's not then its different). You should notice big differences in range and tone color within 6 months. I expect that after 3 months of lessons my male students (age 16+) will have at least an octave and a half range. I prefer to see a 2 and a half octave range when they use their falsetto. After 3-4 months I expect that my females (age 13-14+) will have a one octave belt range, be able to make non-airy sounds in their head voice, and when combining the two have a two octave range. By six to nine months I expect that my females can mix efficiently and can control the usage of their chest voice in legit and belt repertoire.
Hope that helps.