It's not that clear-cut really. Christians can grow and have a benefical time in both private and public schools. The private school is better resourced - so what? Public schools are not that bad.
Your main concern should be how your kids are going to be better wittnesses for Christ and to be able to grow. A private school (especially a religious one) is going to be more sheltered. That can be a good thing for younger kids, however for those in high school not really. A sheltered school-life is not necessarily wise. The real world is going to hit them eventually and they need to be prepared for it. Getting exposed to it in a school envrionment is a safer option, however you're going to find this in public schools more than private schools.
Another interesting point, on average, students from public schools do better in the HSC and at university than students at private schools, despite private students having paid (in some cases) $20,000 per year for all these flashy resources and buildings. You've got to ask yourself - is it really worth it? There can also be a lot of peer pressure in terms of money in a private school, as they are generally more materialistic, generally attracting the higher socio-economic parents. You need to be prepared for that, apparantly it can get quite nasty.
Even in the best religious private schools, there are many people there that are not Christian, and are openly atheist. Don't be deceived that it's going to be like a youth group with lessions.
Now yes, I did to go a public school - all 13 years of my education. However, I know many people who have been to private schools and so I know what goes down in them.
Coming back to my original point - where is better for your children to go in terms of living for Christ and growing in their walk? That's for you to decide, however I"d lean towards public schools. There is a higher proportion of non-Christians there that really need salvation. However, that doesn't mean that there aren't Christian groups and all that there. In my grade of 200, at least 50 were committed Christians. That was a very solid base for us to be good wittnesses for Christ, and honestly it was amazing. Yes, people in private schools need saving too, but I think there is more of a priority for public schools.
The presumption that there are more alcohol, drugs, smoking and sex in public schools I don't think is a fair one at all. The number of crazy parties that have at least a few of the above, that are hosted by private kids is amazing.