I am rather surprised at your choice of the Joker in the Batman film as your choice of villain to compare with Iago. The thing that surprises me is the way that throughout the play, Iago pretends to be something he is not and uses that to manipulate and fool others into doing what he wants them to do. One of the most famous lines from the soliloquy you have identified above is the final sentence, "I am not what I am," which captures the way that there is a crucial and massive difference between the outer Iago and the inner Iago. Iago's evil, therefore, lies in the way that he feigns loyalty and service to Othello whilst all the time using that as a guise to plot Othello's downfall. He is therefore a kind of hidden enemy, that Othello does not know even exists.

By contrast, the Joker is an obvious villain that makes no attempt to try and hide his villainous nature. It is clear that he is evil and he makes no attempt to try and hide this. The one point of comparison that you could perhaps draw between the two characters is the way that both characters, in the words of Iago, "follow myself" or themselves in pursuing their own particular goals or desires. Apart from this, I think there are more differences between these two characters than similarities.