Answer:
It can be, it really depends on which curriculum you use. If you are doing internet school, it is harder. I think the level of difficulty of homeschooling depends on who you are and how motivated you are. A very good math curriculum is called "Saxon Math".
There really is no correct answer to that, as it just depends on what curriculum you use, if you use one.
Meaning no offense in saying this, but I think that public schools' approach to learning is very ineffective. They are loading kids down with homework, and it's getting them no where. I am a homeschooled kid myself, and cannot stand to be around public schooled kids my age because they are just so stupid (compared to me anyway). The way public schools are approaching learning is what I would call "the memorizing method". They drill facts and theories and equations into kids' heads until they memorize it. This is a HORRIBLE way to learn. Have you ever heard more than 10 kids say that they LOVE learning at school? No, not school, LEARNING at school. You can easily say "Hahaha! Who would say that anyway?!?!? Everyone dislikes learning! It's just NOT FUN!". Actually, the way we are learning is not fun. When we are little, before we've been taught that we disike learning, we want to get into everything! Touch, feel, taste, listen, smell, EVERYTHING! People are naturally curious and do, indeed, like learning. Learning should be fun, hands-on, and interesting to us.
I won't argue with you that some homeschoolers are idiots. I will also agree that there are some complete genuises who have gone to public school. It just depends on YOU.
I would say that public school is harder, because there is usually a lot more work. But on average, homeschoolers are smarter.
It's not harder than public.