Public schools are better
The public schools here are absolutely awful, especially the disciplinary system. A kid bullied another student? Better suspend the one who was bullied! It's happened to me before, and that's the reason I'm homeschooled.
I was home schooled until grade 3. It didn't help a bit when I went to public school.
While public schooling is likely less of a hassle overall, it looks to me like they're slowing down the students who are ahead. When shifting back into a public school system due to all the record-keeping involved in homeschooling through high school, my sister was forced to retake Algebra 1 despite providing proof that she was perfectly capable of taking Algebra 2 in 9th grade. This year the school system attempted to force her out of Algebra 2, claiming that she wasn't capable of taking both AP Geometry and Algebra 2, despite her being the top of both classes.