As an indicator of whether schools are delivering on their promised educational services, market share may be an indicator, as Lyndalyn says. Where parents have opted for public schools over other alternatives, there is evidence that some expectation is being met — though it may be price or convenience rather than quality or service.
The fundamental problem in these analyses is the assumption, deep down, that the children belong to the public school systems. Why else would we speak of children being “lost” when they go somewhere else? Is the tax-funded school system entitled to a certain population of students?
If we saw the public schools as a government service for those who did not have access to private alternatives, we’d see the whole thing very differently. We wouldn’t fret that usage of the government service is declining — we’d rejoice that more and more families are finding ways to take care of their own needs. I simply can’t believe that a society with the resources to build public facilities to educate 85% of the children can’t find the wherewithal to do the same in the private sector, given the taxes were returned to the families and businesses now funding the schools.
And I have yet to see a government service do a better job than private providers except in those things which are inherent functions of the state — to establish justice, ensure domestic tranquility, and provide for the common defense. (Promoting the general welfare, to me, means basically the government mostly just stays out of the way — and nowhere is this more true than in education!)