In Brooklyn, a major issue is vouchers. "We pay property taxes, but that money goes to public schools we don't use! Why can't we get it for our yeshivas?" is the rallying cry. As someone who attended six public and two private schools in four different states between the ages of four and sixteen, I wouldn't push too hard for it.
1. Yes, private prep schools invariably show better test results than public schools. But why? Is it because they have resources provided by wealthy donors? Is it because they can cherry-pick students based upon test scores, grades, and recommendations? How many private schools can exclude learning-disabled, developmentally-delayed, or autistic students who don't test well? Public schools have to take anyone who walks in the door. No exceptions. Even if the school is full to bursting, they must take every child.
2. The per-student funding cited by the pro-voucher crowd not only goes for textbooks and teacher's salaries, but for library books, physical plant, school nurses, administrators, office equipment and maintenance (someone's got to keep the Xerox machine running for all those lovely forms), security, resource room instructors, gym equipment, art supplies and other miscellaneous expenses. Each child given a voucher represents a loss of funding to the school as a whole, and will result in an even more unequal distribution of resources than already exists. Those parents most likely to obtain vouchers are those who are more aggressive, wealthier, or more politically connected--and whose children are groomed to be successful in school. Meanwhile, everyone else is left in decaying buildings with broken windows, inexperienced teachers and out-of-date textbooks because of a perpetual lack of funds. (I went to a school like this--it was the tail end of inter-district busing to enforce Brown v. Board of Education in Tampa, FL.)
3. IN NYC, a city that regulates the size of a soda, no government official is going to hand over money to a school without a lot of regulations. If money for private schools come from the same kitty as public school funding, why would anyone think that the same rules wouldn't apply? Particularly for yeshivas where teachers are not certified and secular subjects are disdained or outright ignored, this regulation could lead to a Hobson's choice--intense restructuring including replacing the entire teaching staff with certified non-Jews, or giving up badly needed funds.
In my life, I have attended schools that ran the gamut from beautiful, loaded with amenities and well-funded (Las Vegas--your gambling dollars go to public schools and libraries), to schools which had broken windows, geography textbooks that were a decade old (and this was in 1993--think recent breakup of the Soviet Union), a music program without instruments or songbooks (we had to provide our own), and more students than desks in some classes. I attended a private prep school that had the same read-the-chapter-answer-the-questions-none-of-your-lip teaching style that I thought I'd left in public school. There is no guarantee that an expensive education is necessarily better. However, there is a near certainty that pulling out both money and successful students from public school cannot be good for education as a whole.