A few years ago when I just started learning piano I compared
the rates between private and school and to me I found that private
tutors:
-are cheaper
-more flexible schedule (can cancel here cancel there, shift
around), school you miss one lesson have to usually produce MC, not
always have makeup lesson
-theory do at own pace
etc.
For me I found a younger teacher = less experienced but also
cheaper, and probably more flexible than those teach many years
already.