Difference in quality of teaching between lessons in school and private lessons

Praise be to Allah.

What the teacher must do is do the work that is required of him, and not fall short in explaining things properly, whether he is teaching in the school or elsewhere. What some teachers do, whereby they fail to explain things properly in school but they explain very well elsewhere, is a kind of betrayal of trust and deceiving the students and the school. 

But if he does his work properly in both places, but he does a better job in one due to external factors such as having more time and fewer students, or because the students are smarter or of a similar level, and the like, then there is nothing wrong with that.