There are good and bad charter schools, and good and bad public schools. Our California public school has an API score of 930 out of 1000, which puts it in the top 10% of schools in California. It is a fairly wealthy school, although 30% of the kids are on the free lunch program also.
We have huge volunteerism. The joke is that for parent-teacher night, 3 generations of the family show up. 30% of our school is Asian.
Volunteerism is a huge factor, I think, in any school's success, charter or public. Public schools on average outperform charter schools, but there are exceptions. Many charter schools are disorganized and poorly run, and are not better than the public schools they left.
Students whose parents enter them in a lottery to go into a charter school (but don't get picked) outperform kids who didn't apply, even though they are stlll at the same public school. Why? Likely because parents who are trying to find (what they perceive to be) a better school for their child do other things in their home like getting them to bed on time, encouraging reading, etc.