Also, where we are Montessori was no more expensive than a Catholic private school. But to my eyes, the Catholic school just looked like public school, but obviously more upscale (and also teachers have more freedom, small classrooms).
But I was attracted to to Montessori because of the methods. For example, if a child is focused on an activity, the teacher will not interrupt them just because 'geography hour is over' or some arbitrary boundary. Letting the kids develop focus and concentration at an early age was a big selling point for me.