From the point of view of knowledge and learning, I would say none. I think the real benefit of public schooling is easy access to clubs, activities and resources that many homeschooling parents can't easily provide. The local elementary school where I live provides so many different programs but the academics are mediocre. I homeschool through a charter school and they provide classes twice a week, which is really great. My child gets the benefits of both schooling and homeschooling, so it's the best of both worlds.