Public in my opinion. You still learn and you have a better social experience. In a private school, you're stuck with the rich kids. (Mainly) Don't get me wrong, the educational experience in private schools may be better, but consider everything in public schools.
Depends on where you live and what your values are for your kids. First between the USA and England/Europe those two terms mean very different things so i am answering from the American perspective. Here public school is the government provided and required institution that are, technically free and there are some very good ones and some really really bad ones and everything in between. Private schools here are owned and run by private interests like religious organizations and usually cost a butt load of money to attend and are often fairly exvlusive yet there are good and bad there as well. Many people prefere private schools because they believe theyll provide a better education and, if religion based, will include Christian curriculum many parents want if they can afford it.
It can depend on the school district, in regards to public school. But the way all the systems are now, homeschool (depending on the family) is a better way to go. Homeschooling has shown to be a bit better than public schools for the most part. Higher GPAs, test scores, etc. because of less distractions, more quality one-on-one time with the teacher, and so on. I was in public school from Kindergarten through 5th grade, then homeschooled from 6th on until I graduated. As for private schools, I really don't know much about them.
Depending on the school, private schools have a better system but stricter rules. For example, I know a private school that requires girls to take a pregnancy test every other month. However, many private schools will terminate students that bully, unlike public schools that can only suspend the students for a minimal amount of time.
Public schools have less strict rules and don't require a high payment for your child to attend. However, there is more bullying and depending on whichever school you're going to teach your child. Depending on that school will determine if you child will get the start they deserve.