This would be an option I'd do, if my skill was actually better than what the other instructor is teaching. If you're better and you don't want it to be a big deal, subtly suggest something like it and let it spread on its own throughout the students themselves. Show why it's better the way you teach it in real situations because you do have the better practical experience. Say it to a couple students casually. Let them come to the decision on their own. You are an instructor and are within your rights to offer how 'you' would do it differently. If he starts to cause trouble that would be detrimental for the school in terms of student treatments (being too harsh on them, for example) or something else, go higher than him and state the situation. He's needlessly coming down on the students or whatever and it started after more went to your class than his. That you feel that if this is the case, it shouldn't be allowed to continue.
This is completely machiavelian and underhanded and that's the point.