Ok let me reiterate the significance of the voucher studies.. because there seems to be a lack of comprehension on why it is significant to this discussion:
As already pointed out, comparing average scores of all students in public vs private schools is highly unscientific, because private schools are more selective about their students and because of socioeconomic standards.
More realistic: take the same kids or at least similar kids and compare their individual performances in private vs public schools. This is basically what the voucher studies have done, because the question is one of whether the vouchers are giving the same kids a better education. In general, the answer is no. There are occasional things that would seem to indicate that private schools have a slight edge, but in general the difference is not significant.
I think, however, there is definitely something to be said for a good environment. Regarldess of whether or not the education would be better, I probably would be less self conscious if I had gone to a private school where dope-fiend athletes weren't allowed to hang out at school entances and harrass students while two kids were fighting elsewhere and gathering attention from school officials.
Regardless, I don't think it is valid to say that public education quality is significantly worse because of the findings of the NEA (which have been backed up by other studies). We can show all kinds of statistics saying that a decent private college "Teaches" better than a public one because the average students score higher on the ACT, but this has a severe logical flaw since the students are significantly different.
There have been studies which provide extremely convincing evidence of ways of educating children in the current public school system that greatly improve the quality of education, far more in fact than private schools. One such program takes a different approach to "Remedial" learning, wherein instead of going slower, it goes faster and sets a goal for when these same kids will be at the same level as their peers. The studies of this methodlogy have shown GREATLY improved test scores for these kids.
Another, well-known, method of increasing quality and interest of education is reducing class sizes.
Regardless of how much it costs per student, private schools typically charge more for education when all is said and done under the voucher system. This means that in a way, it is actually more expensive per student. This is after factoring in costs of books, supplies, and tuition itself.