I was educated in the UK from age 5-11 in a state school, from 11-16 in a private school then moved to the US, so age 16-18 was a public school. I have worked in the English education system for the past 7 years.
I enjoyed my years at private school most - the education was pretty broad with great opportunities that didn't exist in state schools - Latin & Greek for instance. The school was small enough that everyone (students and staff) knew each other and there was a genuine family feeling. I felt that I was able to express myself fearlessly.
I don't have any personal experience of home schooling, but it works very well for a friend of mine and her kids - she is careful to ensure that they interact with other kids at social events, so they don't feel isolated.