Two studies have looked at the performance of students in New York City charter schools compared to a matched group of students in public schools. The CREDO study matches students choosing charter middle schools with the performance of a similar group staying in traditional middle schools, using the same procedure it applied to schools in other cities and states. (See here for more information on this study.)
A study by a team led by Carolyn Hoxby compared the results for students who applied to charter schools and were accepted and enrolled to students who applied and were rejected in a lottery.
Both studies found that students who attended charter schools did better than their peers in traditional public schools.
Hoxby has been outspoken in her criticism of the methodology used in the CREDO studies, both in correspondence to CREDO (reprinted on the CREDO web site) and in her report itself.