Tim Challies has written this post about homeschooling versus public schooling, and of course the post elicited quite a few responses, including some nasty ones. A lot has been written on the subject of how Christians should see to the education of their children, and much of it has been polemic.
I think the solution to the problematic question is rather simple. It goes something like this- if you raise your kids with mostly biblical imperatives and few biblical indicatives (in other words, with mostly the law and little of the gospel), sending them to a public school would be a very bad idea. If you raise them focused on the gospel (the indicatives), not sending them to public school would be a very sinful idea.
I understand there will be exceptions based on locale. Our own kids have attended both private Christian schools and public schools. When they were in second grade in Rio Rancho, NM, and the secretary's lesbian partner came to the office and sat in her lap while they made out, we decided that private school might be important in that locale. When we lived outside St. Louis, MO and here in Canyon, TX, the public schools have worked fine. So in general, I think kids raised on the indicatives of the gospel will approach their secular world (still as sinners, of course) with the right attitude of being witnesses of their Lord and savior first rather than serving themselves. Of course there will be mistakes. But learning to live in a secular world will be fraught with mistakes no matter which direction you choose for them, and this way (living in light of the indicatives of the gospel) will give them a much better path and foundation to choose what is right based on what's in their heart rather than because it's the cultural thing to do.
There's a spectrum somewhere between the tiger mom and the dad in, 'A Boy Named Sue' where raising kids works best. But I don't think it's a narrow line nor hard to find. I do think we are all prone to extremes one way or the other, however, and that's what makes raising them difficult.