As soon as Dumbledore emotionally burst out and physically pushed Harry back while exclaiming "Did you put your name in that goblet?!", I knew this was a completely separate Dumbledore from the books.
But to be fair, Gambon was playing the role the script and director determined. If Dumbledore had been written correctly for the 3-6 films, I'm sure Gambon could have pulled that entire persona off very well.
The representation of Dumbledore is only half the problem of the films. The other half is Voldemort. Instead of having a villain that is legitimately intimidating, we have something that borders on the cliche. He's every bit how you would expect the main antagonist in a young adult animated series to act. Voldemort in the books is introverted and gathered. And when he becomes angry, it's white hot. He lashes out like the serpentine man he is. There's tension in every scene, because you never know when he's going to lash out at Wormtail, Malfoy, or Bellatrix for whatever petty reasons he sees fit.
When Fiennes as Voldemort becomes angry, such as in the graveyard scene of Goblet of Fire, he's over-the-top and sometimes embarrassing to watch. I use Goblet of Fire as a reference for the problems of Dumbledore and Voldemort, since while it's my favorite film of the series, it goes far in giving us scenes that bring to light the creative faults of both character incarnations.
They dropped the ball with the two most important characters besides Harry Potter himself, and for that, the films will never come close to measuring up in comparison to the books. This is usually the case when comparing a book turned into a film, yes, but the quality gap here is especially noticeable. They could have done a hell of a lot better; given their budget, given J.K. Rowling's guidance, and given the fair amount of time they had to prepare.