It's interesting that Harry's handwriting looks so much more forceful and certain than William's. I make no pretense at having any expertise in handwriting analysis, but to my unschooled eye, William's looks like it was written by someone who is pretty much ungiving.
The two examples are really apples and oranges. William's is a quick note of thanks in a hotel guestbook while on holiday, whereas Harry's is an official public tribute to victims of a terrorist attack. Depending on the context I think most people vary their writing in much the same way they do their voice when chatting to one of their friends on the phone versus chatting to their boss on the phone. Everyone has a 'telephone voice' and, I suspect, we all have a handwriting equivalent.
From my personal experience, left-handed people tend to have somewhat messier/disjointed handwriting when compared to right-handers. Probably a massive overgeneralisation on my part.