DS is in public school, last year was kindergarten next year is first grade. I love the elementary school he's at right now. We moved halfway through the school year and I'm so happy we're in a better school district now. IMO if the district is good, public school is wonderful. They get a lot of interaction with their peers without the cost of private schools. If it's a good district the education is the same if not better. We plan on putting all of our children in public schools.
Right now I'm doing online school. Pros? I get to stay home with LO 24/7.
Cons?Pretty much no social life.
When I was going to school: Pros? I got to talk to people. Cons? Getting up and getting LO ready.
But if you're referring to a younger child, go with public school.
Unless later they have problems with people/school
Private schools are usually far and away better than public schools. Cons: a middle or lower income person barely managing to send their child there, because it's a priority, may find that there are difficult class differences to negotiate.
If you're in a city (major city)--homeschool or private. Don't think about public unless it's some kind of amazing magnet that you won the lottery to get your kid into.
Homeschooling is hard to go it alone w/o support on finding good curriculums and teaching tips and social groups and stuff like that. I can't imagine doing it w/o major support. However, I can definitely imagine doing it. I think it's probably what we'll end up doing for early education.