I have a similar personality to my son who i think would benefit better from a private school. I failed at school and not because i wasn't capable, i know i certainly could have done all of the work put in front of me. The problem was i had a bit of a short attention span and no one even came down and sat with me to make sure i was doing what i was supposed to be doing. I would rather sit there and chat with the other students who were exactly the same as me not doing their work, or make some excuse to leave the room to go elsewhere where i could get out of doing it. This is where i think a nice private school would be better for him, i believe he would get more attention and be with other students who's parents would be giving their kids more attention and making sure they do their work. I'm not saying of course that there aren't students with parents who care in public schools but the truth of the matter is occasionally you do get a family where the parents don't care and just send the kids to school because its the law and to get them out of their hair. Its these kinds of students who would unfortunately end up being a bad influence on others because the teachers aren't well funded enough to give these students the attention they should be getting from the parents. I also believe that you are far less likely to come across these types of disruptive influences in private schools as parents pay so much for their kids to go and its always because they want the best for their kids and they usually are willing to put in the time and effort as well as the money to see that their child gets what they need.
As i said before i also think it depends greatly on the child. I'm not ruling out public schools as any kind of lower education. My second child is a really sweet little boy and i believe he would do well at a public school. He's got a much mellower personality and i think it would be easier for him to do his work, work a little more independently and not get so easily distracted.
Its really more about the atmosphere of the school. A smaller school like ones you would get out further into the country i think would also be great for giving students the attention they need to achieve even though they might be a public school, unfortunately where i live though all the schools around here are the government funded over crowded ones where just about anything goes.