A key problem with using public tax dollars for vouchers for private schools, there are a limited number of seats in private schools. That puts the ‘choice’ into the hands of the school, not into the hands of the parents.
Vouchers are also sold as a way to provide choice to low income students. However vouchers rarely cover the cost of private school tuition. So, the voucher money becomes a discount for private school for high income families who would have paid for private school regardless of the voucher.
Below are some great articles that discuss how vouchers have impacted students in the states where vouchers have been implemented.
Please add any other pertinent links in the comments below.