There are negatives and benefits to both and part of that type of decision would depend on where you live and how committed the parents are (for both home-schooling and public schooling).

Home schooled parents need to make sure their children get socialized, and not to generalize to much, but most of the home-schooled kids I've ever met were kept away from non-homeschooled kids (unless in some sort of religious community). That's not ALL homeschoolers but that's why sports spots have specific home-schooling classes because the parents won't put them in with non-homeschooled children. The point of homeschooling can sometimes be to keep their kids away from bad influences. Not necessarily a bad idea but brought to the extreme where children aren't allowed to even assosiate with other kids even in a supervised 1 hour a week program seems extreme to me. Or having certain kids that a child isn't allowed to play with on the same street (which is what happened with my home-schooled cousins) is a little strange to me.

On the other hand for parents who's children are in public school in general the parents need to be the ones to make sure their childs being fully educated. If the child starts to fall behind his/her peers it's up to the parent to get the child up to speed, even though they believe the teacher is responsible. Home-schooled children will get a lot more individual attention than a public school child. Children in public school are influenced more by their peers simply because they are around them longer than they are their own family. If a child spends 8 hours at school and then goes home for 5 hours until bedtime, he's much more likely to start doing what his 'cool' peers want than his parents. I have a friend who's in high school and when she was in grade 8 HER friend was talking about how she punched a girl in the face. I asked her why and you know the response? 'Because I felt like it'. These are the children who YOUR child is going to be spending their day with. Either they will be on that childs side or possibly on the other side. Which do you prefer?

Personally I think private school would be the best of both worlds. Your child is being socialized in a setting where their are (usually) smaller class sizes, more individual attention, nicer children (a private school doesn't 'have' to keep the type of kids public schools do). There is usually more space for your child to breath academically and more support if they are struggling. The teachers actually care what the parents think because basically you're a customer and more. Unfortunately that isn't always affordable, just like home-schooling isn't always affordable. The real question should be why do we have people home-schooling and sending their children to private schools when we should have a proper public school system? A large percentage of people are upset with the public school system and yet everyone just takes it at face value that this is the way it's supposed to be. It just seems weird...