He's been weekly boarding at a state grammar since he was 11, has loved it and has developed hugely as a person. It wouldn't be for everyone - certainly not for my middle son, who is less socially aware than his big brother - but it worked for DS.
DS is 15 now, & especially likes the freedom to build his own social life in boarding. When he was younger, the alpha mums were absolute tyrants at the school gates. There was no Facebook, no smartphones, Mumsnet etc just starting out - so if your face didn't fit then your child bore the brunt of it, day in day out.
DS is very personable and easygoing, and was frustrated by the lack of social opportunity. Boarding schools these days, including the state ones, tend to be much more diverse than day schools. It suits him.
Whether you go for day or boarding, the main thing is, of course, that a child is in a place where they feel accepted & where they belong. Grades aside, people often underestimate the role that strong friendships play in a successful education.