Indiana University has conducted what seems to be the first major study of charter schools in Indiana. Maybe it's too soon to expect definitive answers, but I didn't find it very helpful:
"That said, we hear often from critics who say that charter student achievement is very poor compared to traditional public schools," Plucker said. "We don't see any evidence for that conclusion. At the same time, we often hear from advocates that charter student achievement is much better than that for traditional public school students. We don't see any evidence for that conclusion, either. The truth, as is often the case, is probably in the middle."
The study can probably be cited by charter advocates and critics alike, which means nobody should rely on it to support one side over the other. I did find this interesting:
While there is some innovation in charter schools, traditional public schools seem to be creating new programs in response to charter schools in the district. "You are seeing districts begin to make some changes and to be more innovative," said Akey. "Whether that's a direct function of charter school innovation or just charter schools being there, that's not clear."
The hope for charter schools is not just that they will be innovative but that they will also spur other public schools to make changes to be more competitive -- without resorting to a full-fledged voucher system that sends public money to private schools.