Prince Philip was made of different stuff from his son, for a start he'd had a very peripatetic upbringing, he'd been in active service during the War, all of which I imagine developed his tough nut exterior, Charles on the other hand has been presented as sensitive and not overly confident as a child.
Gordonstoun sounded a ghastly place and allegedly Charles unsurprisingly was very unhappy there, I think most kids, unless made of sterner stuff, would be. What is it with fathers who think their school toughened them up so they must subject their son/s to the same very spartan rigours, I've even read about such men having boarded themselves, knowing about the sexual abuse that went on, merely regarding that as par for the course, "something one is expected to put up with"
When young children are sent away from home they're isolated, they don't have a voice. It's not only boarding schools, sexual and physical abuse has been rife in orphanages, children's homes, they seem to be a magnet for sadists and paedophiles. Testaments of those who have survived these places are often adults who carry the scars on into their adult lives.