I would rather not watch or re-watch any film by either Lucas or Hooper, so I can't agree that collaboration made their films better. I have found them all questionable.
You used a quarterback as an example. I would use a head coach and stick with the same team. The team has dramatically overhauled its roster since Belichick has become the coach, but they consistently rank as one of the best teams in the league. I am sure you would be quick to point out that Brady has always been the constant, but even in his injured year they went 11-5, a feat few teams accomplish each year. Conversely, we have seen great players leave a coach and fail to repeat their success elsewhere. Donovan McNabb and Kevin Kolb looked great in Philadelphia and flamed out elsewhere, while Vick looked like a good quarterback for a few years before it all fell apart.
You can see the influences of smaller parts in films, to be sure. The dialogue of The Social Network was vastly different than what is usually in a Fincher film, thanks to a different writer. Paul Thomas Anderson's The Master was his first not to use the cinematographer Elswit and it had a different look. However, unless you are actually on the set of the shoot, there isn't a real way to say so and so film was directed better but some other film is better. Like the head coach or a CEO of a company, the director gets the credit or the blame.
Okay, I agree with a lot of that, but I think the awards represent two different distinctions. Best Picture recognizes the entire production for their work on the film, more of a team award, and Best Director recognizes the director's efforts, more of an individual award (in sports, sometimes the coaches who win coaching awards are not coaches of championship teams). The director's contributions are one part of the whole, and while they'll often get overall credit for it, there were more contribution's to the films final output than just their work. I don't think the awards are the same thing.