There is an age-old debate in our fandom, one that has been raging ever since the theatrical release of Harry Potter and the Prisoner of Azkaban in 2004. Richard Harris - the phenomenal actor who had played the role of Albus Dumbledore in the first two 'Potter' films suddenly passed away before the shooting of the third movie and was quietly replaced with Michael Gambon, a legendary actor in his own right.
Since the replacement, there has been some degree of controversy. Fans have often claimed that Gambon-Dumbledore does not exactly capture book-Dumbledore - and in some film sequences this difference is more, shall we say, highlighted than in others.
Fans may remember a key scene in Harry Potter and the Goblet of Fire when Gambon-Dumbledore becomes very... agitated, when confronted with the fact that Harry may have cheated to enter his name into the Tri-Wizard tournament.
On some level, this question is almost impossible to answer - perhaps even just a matter of opinion. And yet, from all the hardcore 'Potter' fans I've ever spoken to about this question Richard Harris' version of Dumbledore emerges as the true favorite, while Gambon's performance is consistently viewed in the negative - (with fans regularly citing the scene above!)
There is an argument in the fact that Richard Harris, due to his age, (72 at the time of his death) likely wouldn't have been able to perform many of the battle sequences that took place in the final films, so could a Harris-Dumbledore supporter argue that Michael Gambon was a truer Dumbledore in body and Richard Harris in attitude or spirit?
Given the fact both actors portrayed the wizened old Dumbledore to the best of their ability, perhaps we can't really say one did a better job than the other. At the end of the day we need to keep in mind answers to these questions are essentially going to be different for everyone.
For myself, I've always favored the Richard Harris version. Sure - that may be because I grew up with that Dumbledore in mind, given that was the time I was first introduced to the magic - but I would say I'm also biased against Gambon because he never read the Harry Potter books.
But hey, I'm a purist. :p