That is a very interesting question. I would say one point of comparison would be between Beatty and Iago. Both are wily, cruel, and deceptive people who work against the interests of the main characters of their respective works.
Beatty betrays Montag by not telling him that Mildred has turned him in and that it is Montag's house they are going to for a book burning. Beatty is arrogant and quick to quote from the banned books he despises. He thinks he is smarter than Montag, taunts him, and is ultimately killed by him.
Iago likewise betrays Othello, though in his case, he utterly fabricates the situation of Desdemona's supposed affair with Cassio. Nevertheless, like Beatty, he is deceptive, cruel, and underhanded. Like Beatty, he is arrogant and thinks he is smarter than the people around him. Like Beatty, he carries a chip on his shoulder that causes him to lash out maliciously at people. Like Beatty, he is killed at the end by the work's protagonist.
Both works also illustrate the importance of deeply questioning and exploring the world around you. Montag's civilization is destroyed because too many people have unthinkingly accepted what their leaders have told them and allowed themselves to be lulled into thoughtless, superficial lives. Iago is able to win Othello's trust and lead him to destruction because Othello is too trusting and allows himself to believe what Iago has insinuated without asking enough questions or exploring what is really going on.