The other day a customer quoted a prominent trombone player as having said "Play the largest mouthpiece you can."
I pointed out that the player to whom the quote was attributed did not play a particularly large mouthpiece. Does this mean that the quote was misattributed, or that the person was not following their own advice? I don't think so.
Other equally prominent players give the advice to play on the smallest mouthpiece you can. Are they offering an opposing view? I don't think that is really the case either. I think they are saying pretty much the same thing, when you fill in the unstated provisos.
I think the intent of their advice is to recommend playing the size (whether large or small) that gives you the best balance of sound, response, range, endurance, comfort, and flexibility to meet your specific needs.
This means striking a balanced compromise between mouthpiece features that might have opposing effects. Where that balance is found depends on factors specific to the player's own situation. It will depend on their priorities.
Some players will lean towards a mouthpiece at the lower end of their usable size range and some will lean towards something at the larger end of the spectrum. Their choices should reflect their abilities, challenges, natural tendencies, and playing situation.
The most common issue I see, especially with amateur players, is using a large, deep mouthpiece. It gives them an extra full lower register at the expense endurance and a good sound in the upper register. They have not found a good balance.
The trombone player to whom my customer was referring is an orchestral player who uses a mouthpiece with a larger than average diameter and a shallower than average cup depth (for an orchestral setting). Are there larger, deeper tenor trombone mouthpieces? Absolutely. Could the player in question play one? Yes, but a deeper cup presumably would not provide the balance of performance characteristics they need. So he does not use the largest mouthpiece he can play. He plays the largest mouthpiece he can, optimally.
That is an important distinction that in my experience many players should carefully consider.
Dr Dave