Charter school students have told reviewers the state schools they used to attend were "dumb" and "boring".
And a teacher from one of the publicly-funded private schools has accused regular schools of sending 'problem' students to their school.
The comments were included in the first independent evaluation of charter schools, which has given the publicly-funded private schools a pass mark for innovation.
The report by consultancy firm Martin Jenkins was commissioned by the government and considered whether three of the first five schools set up in 2014 were doing anything new.
It said the schools' governance, management and use of funding was innovative. The schools were governed by people selected for their expertise, rather than because they were parents, and management was split between a chief executive and a principal in charge of education.
It said those innovations would help foster developments in other areas.
"There are some early signs that the case study schools/kura are developing innovative educational provision for their students. It will be critical to see to what extent innovation grows in coming years, and as schools/kura learn how best to respond to students' needs and aspirations."
The report said the three schools showed "multiple examples of best practice" in teaching.
"While similar examples can be found in state schools, these practices are not widespread across the state sector."
The report was based on site visits to the schools and interviews with their staff and students, the schools' documents and reports, and Education Review Office reports.
It said teachers and principals at the schools were highly motivated.
One told reviewers their school did not want to grow much because its success was related to its small size. Another said their school's approach would not work with middle or high-achievers.
One teacher said charter schools' freedoms give them an edge over state schools. But another said they were not treated fairly: "Other schools are funnelling their 'problem' students to our school - that's not really fair."
The report did not consider student performance, which will be examined in a future evaluation.