Richard Harris didn't read any of the books either, and I'm fairly sure Gambon has read PoA, as he said so on the DVD, so if anything, he understands the character more than Harris. As for his GoF role, I don't like his sudden violent behavior in the trophy room any more than most do either, but I digress. I like Gambon better, even though he can be over the top sometimes. He brought more excitement than Harris did, I admit, but lost other traits.
I think the best Dumbledore overall was PoA. He was fantastic. Personally, I thought he hit the nail right on the head. Gambon brought that sense of quirkiness and humor to the character. Richard Harris had the calmness down to a tee, but Gambon has the eccentricity that Harris didn't have. I felt Harris was far too old to be playing Dumbledore. He always made Dumbledore seem breathless, sick, and senile. No disrespect to the actor, but I honestly couldn't imagine him doing what the character does in the later books, like doing breaststrokes. In my opinion, Gambon played a better Dumbledore (mostly in PoA) and did a decent job in setting him for what's to come, though I kinda pictured Harris talking in the astronomy tower when reading HBP, not Gambon. DD may have been nearly butchered because of that little stunt in the trophy room, but I think this was mostly due to the director and the script. I can only hope that the new director will fix this, and I'm very optimistic about him. Yates seems to know what he's doing and has gotten pretty much nearly everything right so far.
I'll admit, however, Harris had stronger presence than Gambon.
