Depends totally on the school and the child.
As someone who has been educated in, and taught in both, it comes down to what you want for your child.
Private schools are expensive, class sizes are smaller, teachers may not be qualified, there may be greater opportunities, behaviour can be worse, in a different way, it may provide openings depending on who you know, the education isn't always better (I had the most awful, uninspiring teachers).
State schools are generally larger, more in a class, more support staff, higher level of SEN, behaviour problems are different but exist, I find teachers tend to be more inspiring, less openings for future but that didn't get me anywhere anyway. Children and social aspect of it are more down to earth and generally nicer.
Of course, these are massive generalisations as every school is different.