I think the biggest indicator of William and Harry's relationship has to be the way they've chosen to work together in official capacity. Yes, they each do a lot of things independently of the other. But they created an office at Kensington Palace to share, they've found ways to coordinate their charitable focuses (and Kate's) into an overarching theme of mental health, and they've worked together on several occasions to organize large events such as the Concert for Diana.
Prince Charles was pretty vocal (well, as vocal as royals get in these situations) about wanting them to stay under the umbrella of Clarence House and he's seemed to allow Clarence House staffers a degree of leeway to complain to the press about the differences of philosophy and strategy that exist between his office and theirs. It seems like a strong statement on their part to step together out of that situation and take charge of their own royal careers together. Even just moving to Kensington at all, when there seemed to be moves to phase out the royal residences there and try to keep more royal apartments on the St. James complex (which is where Clarence House is, right?), seems to have been something of a coordinated power move on their part. They're standing united in their decision create their own charitable work rather than simply take on management of the Prince's Trust, too. All in all, while their father certainly has one model in mind for modernizing the royal family once he becomes king, William has his own ideas percolating for how things should be once he's on the throne, and Harry's working together with him to lay a foundation.
And more generally, it seems to me that there's a pretty sharp contrast between William and Harry's comfort with each other and the way the next generation older operates. Charles and his siblings have acted quite independently of each other from the start of their lives as working royals. It's very rare to see any combination of Charles, Anne, Andrew or Edward show up at the same event beyond the really big ones where everyone is expected to attend to the Queen; when they are together they all seem much more relaxed with the Queen than with each other. That's not to suggest bad relationships or outright dislike, just that they aren't around each other enough to be close. They all circle their mother in orbits that rarely intersect. And honestly, that's not that uncommon in families, royal or not. In contrast, William and Harry do a number of joint appearances every year and it's not uncommon to see them playing polo together or choosing to attend the same sporting event. They gravitate towards each other when they're in the same place, they tease each other, and it's not uncommon for them to settle into a more relaxed posture than the "royal on duty" pose when they turn to speak to each other. They may not be the very best friends, they may sometimes push each other's buttons, but they certainly have a comfort with each other that goes far beyond what their father has with his sister and brothers.
This is one of the most well thought out posts I've read in a long time and totally agree with the insights that you've given. 
