I can't personally speak to public education vs. private education vs. homeschooling, as I just haven't spoken to enough people to get a sense of a comparison.
I do really like the potential for homeschooling - the fact that you should, pretty easily, go way beyond the level of education in school. The film "Captain Fantastic" comes to mind (while it had a moronic scene where a daughter and father were discussing "Lolita," in the ignorant style of the time).
I don't see the curriculum being "state sanctioned" as a particular problem, more so that education in schools is mostly a waste of time for all concerned, especially at the higher levels. It's like it was developed with no knowledge of human psychology - it's almost completely centered around memorization, testing, followed by the quick and efficient forgetting of almost everything memorized by anyone with a relatively normal memory. Memorizing facts, which aren't even retained, instead of learning how to think, reason, critique, compare various arguments or perspectives and coming to your own conclusion.