While I have little doubt that this is the case in the long run, I also don't doubt that in the short run, there are public schools or schooling systems that can leave students better off. Charters are in effect experiments and actual markets where individual schools can do much better or even more poorly than their publicly run counterparts. The difference in charter schools though, is that there's a virtuous feedback loop - that the best survive and thrive while poorly performing public schools tend to live on to deliver immense harm to students. I think this an even more important moral argument to make. Reason.com quoting the study:
Comparing [National Assessment of Education Progress] achievement obtained in public charter schools versus TPS for 21 states and DC, we find the public charter school sector delivers a weighted average of an additional 17 NAEP points per $1000 invested in math, representing a productivity advantage of 40% for charters; In reading, the public charter sector delivers an additional 16 NAEP points per $1000 invested, representing a productivity advantage of 41% for charters.
... The analyses we present in this report indicate that charter schools are more productive than TPS, either because they produce higher student gains at a lower cost or because they produce similar or only slightly lower student outcomes at a significantly lower cost.