They differ in terms of the relationships he has with other characters. In canon, he has a mentor - like relationship with Harry. However, in fanfics that hate him, this relationship can be completely flipped. Harry might see Dumbledore as an enemy or at least a very untrustworthy figure. The other characters' reactions to Dumbledore also change. They might be more critical or even actively oppose him, which is a big departure from the original where most characters respected him to a large extent.
The fanfictions that hate Dumbledore differ from the canon in the way they explore the consequences of his actions. In the books, the focus is more on the main plot against Voldemort. But in these fanfics, the writers dig deeper into the side - effects of Dumbledore's decisions. For instance, how his actions affected the lives of minor characters, like the students at Hogwarts. They might show that Dumbledore's actions had a more negative impact on the overall well - being of the wizarding community than was shown in the original story, which mainly focused on the fight against the Dark Lord.
Fanfictions that hate Dumbledore often deviate from the canon in how they portray his character's intentions. In the canon, Dumbledore is generally seen as a wise and benevolent figure, albeit with some flaws. But in these fanfics, his actions are often painted as more self - serving. For example, his actions towards Harry might be shown as being more about his own legacy or power plays rather than protecting the wizarding world as in the original story.