That's absolute hogwash.
Examples of differences:
- In government schools, incompetent teachers are kept because of seniority rules, in corporate schools, they're fired.
- In government schools, teachers and adminstrators make a "political wage", in corporate schools, they make a market wage.
- In government school systems, failed schools go on forever, in a free market, they go out of business.
- In government school systems, students are told what school to go to, in a free market, students (parents) vote with their feet.
Blink twice if you've gotten a clue yet.