It's all very well to point out that William went through the same thing but they are different people. Years ago, even before Diana's death, someone from the Royal Household said that we shouldn't go by looks as William was a Windsor through and through despite his then Spencer appearance but Harry was the one who was emotional and empathetic like his mother. Remember that Harry was seen as the 'fun one' because he was a natural with children (perhaps even somehow partially arrested there?), mixed easily with people (one Welsh Guardsman with whom Harry spent time on Walking With The Wounded said that he was nervous about meeting royalty but Harry was "just a bloke really"), and generally have a laugh with the public.
In comparison, William has always been more contained in public and, for a father of three, seems rather distant when meeting children out and about.
Even Charles has come into his own as a grandfather, crawling around with his and Camilla's grandchildren according to her, and happily ruffling hair etc of the children he meets out and about. If you watch Charles, he also tends to touch people on the arm when he's talking to them, to make a connection.
To me, William seems more of a throwback to a previous generation; Queen Elizabeth kept herself very much to herself in public and William seems to be that way, except for his temper - and Philip could be explosive at times.