I've been in public school, private/Catholic school, and am now in online school, and honestly all of them are good.
Private was the best for me personally because of the small class sizes, and I was at least 1 teacher's favorite student.
Public was okay, but too chaotic and stressful for me.
Online is good, you work at your own pace.
However, there is a fine, fine line between homeschooling and home'schooling'. You need to make sure you learn everything the way you should/would at a non-homeschool.
Why? Why is there a “right way” to learn? Why not whatever suits the person best? With homeschooling you have a chance at that. In public (or private) you just have to hope your learning styles match what is in the classroom. And if not, too bad.
Yes, the right way to learn covers the CORE classes of science, social studies, math, English, reading, and health/physical education. If you aren't getting those (and extra classes of your choosing, such as religion, drama, a foreign language, typography, business) you aren't learning correctly. Every homeschooling parent is responsible for teaching their kid what they would learn at a public or private school, just from home.
For example, I'm taking Algebra, Biology, World History, Honors English, Spanish 2, Creative Writing, and Gothic Lit from my own home using an online program. I could learn all of those at a physical school, but I choose to take them online.