Wikia quotes Gambon as such:
In discussing his portrayal of Dumbledore in the Harry Potter film series, Gambon has given detailed accounts. Particularly, he was quoted as saying that when portraying Dumbledore, he does not necessarily "have to play anyone". He further states, "I just stick on a beard and play me, so it's no great feat. I never ease into a role – every part I play is just a variant of my own personality. I’m not really a character actor at all." This suggests that Gambon chooses to act his performance based on his own intuitive interpretations of how a character would respond to certain situations. In short, Gambon has not deliberately aimed to follow the specific characteristics of Dumbledore, as referenced in the books, but rather developed an acting style in which he combines his own personality with that of his character. Not only had Gambon not read the books before being cast in the role of Dumbledore, he chose to not read any of the books after receiving the role, as he felt that "Actors can get a bit miserable when they read the book and realise, 'Oh, my scene from the book has been cut.' That's not the point."1
Gambon, in comparison to Richard Harris, has portrayed Dumbledore as a more robust, vocal and rather eccentric wizard. Also highly noticable is Gambon's deviation from both the books' and Richard Harris's Dumbledore in terms of emotional composure. While Dumbledore is mostly described as "calm" in the books, Michael Gambon's Dumbledore appears far less so at times; on some occasions raising his voice in a threatening or angry manner. Richard Harris's interpretation differed in this respect, opting for a far calmer demeanour on his character's part. The films have, so far, not attempted to address this discrepancy between Gambon's portrayal and Harris' quieter, less physically abrupt performance. As such, the Harry Potter series has followed the same path as the 1960s magic-oriented sitcom, Bewitched, which likewise changed a lead actor with no explanation ever offered.
And in another interview:
To what extent did you have to inherit Richard Harris's performance?
No one ever spoke to me about it. Not a word. On the first film I did which was directed by Alfonso Cuaron I walked in there and I'm naturally Irish and my first accent is Irish, I will speak Irish with my parents, and I played just a slight touch of Trinity College Dublin. That light lilt. I did that and Alfonso said, "What's the accent here?" I said, "Irish." He said, "That's OK." And no one's ever mentioned it. I'm a little bit more camp, I think, a bit lighter. A bit more ethereal.
Cuaron himself said this in an interview:
He was, in retrospect, a great choice. He’s similar enough that it didn’t feel jarring but at the same time he brings his own thing. It’s a slightly different Dumbledore than it would have otherwise been, isn’t it?
Alfonso Cuarón: It is slightly different. From the get-go we made changes to give the continuity, but at the same time it was not about imitating Richard Harris. That would be so bad for both: for Richard and for Michael. Richard was very regal - as Dumbledore is described in the books - and very beautiful, and we wanted to do it more hippyish, cheekier and a little more shabby. And sometimes more distracted.