Richard Harris' portrayal of Dumbledore in the Harry Potter series was a very frail wispy old man. In the third movie, when Michael Gambon stepped in, they did a very good job of making him look similar, but it's obvious his speech patterns change from being a little old man to being a much stronger less wispy old man. His booming voice changed the character of Dumbledore. Is there an explanation of why the directors allow this change in an interview or public knowledge anywhere?
I don't have any hard evidence, but there may be a number of factors that influenced the sudden change in character.
The first time we really see Dumbledore as anything more than a kindly old man, and do anything more than general headmaster duties, is during the events of OOTP (Book 5). This was released in June 2003, around half a year after the Chamber of Secrets movie (November 2002), and a year prior to the release of the Prisoner of Azkaban movie (May 2004), which is when Michael Gambon assumed the role.
Before book 5, the novelized versions of Harry Potter contained only rumors of Dumbledore's prowess as a wizard, but had shown no real evidence for it. He was smart, experienced and accomplished, but other than that he was reasonably mysterious.
However, near the end of OOTP, when
Dumbledore battles Voldemort in the Ministry of Magic
this is the first evidence we have that Dumbledore is still a powerful wizard in his old age.
I don't know if the producers were aware of what would occur in the later books or whether JK Rowling kept it a secret, or if she even knew all of it herself at that point, but it's possible that Richard Harris played it in the way that he felt Dumbledore was portrayed in the earlier books.
However, once more was revealed about Dumbledore's character, they may have decided to start to change the character of Dumbledore to more powerful and active to reflect what further information they knew about him and establish him earlier so that it wasn't so much of a shock to audiences later on.
In addition to a new actor playing Dumbledore, the director of the Harry Potter franchise changed from Chris Columbus to Alfonso Cuaron between the 2nd and 3rd films. It may have been the directors choice to adapt the character to what he felt was more suited.
So the character change may have been the actor's decision, the director's decision, a producer's decision because of the new information about the character from the books, influence from the author due to her creative changes or a combination of all of the above, but it is likely one of these reasons. Had Richard Harris continued to play the character, he may have changed how he played it also.