Scaled-up voucher programs like those previously advocated
  by Secretary DeVos show the worst effects. There have
  recently been four statewide voucher programs: Florida,
  Indiana, Louisiana, and Ohio. The Florida study is
  inconclusive, and the others show large negative effects. In
  some respects, the Louisiana results are more convincing
  because the results have been corroborated by two different
  sets of researchers and students were assigned to vouchers
  by lottery—the most rigorous way to evaluate vouchers. In
  terms of providing convincing results, the Indiana and
  Ohio programs, are somewhere in between, but these show
  negative results as well.

  Voucher supporters argue that the results have been worse in
  the recent statewide programs because they have been
  “heavily regulated,” by which they mean the requirements
  that students be tested, that these results be made publicly
  available, and that schools must let in any student who is
  eligible for the voucher. The fact that this fairly minimal
  oversight is considered controversial or heavy-handed,
  however, only reinforces that private schools are designed
  to be exclusive and have little interest in external
  accountability.

I wouldn't expect charter schools to actually change much because the evidence is very clear that the most important factor in achievement, overwhelmingly, is the child's home environment.