The perceived quality of an elementary or secondary school seems to be entirely a function of the socioeconomic status of the students' parents, even if the people perceiving the quality pretend to themselves that such is not the case.
To state this even more simply (though politically incorrectly), poor children ruin the quality of a school.
Suburbs usually have better schools than cities for the simple reason that, through zoning, suburbs have prevented poor people from living there, ensuring that there are no poor children in the suburban schools.
In my view, the advantage of vouchers is that they will allow better socioeconomic sorting of students. This will benefit middle class parents who will be able to use vouchers plus some extra money they contribute themselves to send their children to a school without poor children whose parents can't afford the extra money.
Other voucher supports believe that vouchers will actually improve the quality of instruction by creating competitive incentives. After thinking about this, I don't think this will make much of a difference. Parents probably have no basis to judge the quality of instruction. Parents are only able to judge the quality of a school based on the socieoeconomic status of the other parents.
The supposedly high quality schools in the suburbs may actually have pretty bad instruction, but no one notices so long as the students do well on standardized tests. Test performance is almost entirely a function of the students' innate intelligence, which is correlated with their parents' socioeconomic status. And that is the primary reason why socioeconomic status determines school quality.
Instead of sorting students by socioeconomic status, it would be more efficient to sort them by intelligence. And this is something that vouchers can't really accomplish, but a large public school system can accomplish this by testing students and busing them to a school with students of like intelligence. This will ensure that level of instruction can be geared to all of the children in the class. The discipline problems are almost all caused by the less intelligent children, and they will be congregated in schools where discipline can be the primary focus.
Sorting by intelligence would be the fairest and best way to help poor children who are smarter than their peers, because they would be given the opportunity to escape the ghetto and get a better education.
People stumbling across this post seem to take issue with the notion that intelligence is a trait that varies between children. Please refer to my post NY Times says IQ is genetic.