Here is scholarly paper that uses random assignment to test the benefits of school choice on students' motivation and academic outcomes. Here is another one on the effect of vouchers on college enrollment and its summary in the Wall Street Journal. Both results are positive and contribute to the growing scholarly literature that finds positive benefits of school choice. Of course, not all papers find positive effects but this is social science, so there should be no expectation that they should. Nonetheless, the overall thrust of the literature points away from the conclusions teacher's unions would like you to draw. Here is a far left defense of teachers unions and its evisceration.