Both men are outsiders in Venetian society: Iago in terms of class; Othello in terms of race. They are military men, men of action, who've achieved their place in the world due to their own efforts on the battlefield. But Iago is a deeply resentful man. He hasn't received what he believes to be his due. He hates Cassio for being promoted over him, expressing contempt for a man he believes to be little more than an upper-class dandy, without Iago's hardened battle experience.
But he also hates Othello. The Moor is even more of an outsider than Iago, yet it is Othello who's risen through the ranks, not him. For different reasons, Cassio and Othello stir Iago's deep, bitter resentment. Iago's reached the point where he's effectively given up on being accepted by the upper echelons of Venetian society, whereas Othello still very much yearns for their acceptance. If Venetian society won't accept Iago, then he'll do his best to undermine it, systematically destroying everyone above him—Othello, Cassio, Desdemona, and Roderigo.
The two men's insecurities extend beyond issues of class and race to matters of the heart. Both Othello and Iago are fiercely jealous. Iago is convinced that Othello has been sleeping with his wife, Emilia; this adds further fuel to his already burning resentment. And Othello, for his part, has been persuaded by Iago's crafty insinuations that Desdemona is cheating on him with Cassio.
Both men ultimately come to grief through their inability to restrain their emotions. The difference is that Othello's true self, his noble, decent, trusting self, is corrupted by the insecurities subtly woven into his mind by the scheming Iago. As for Iago, his character has never really changed; he's been full of bitterness, resentmen,t and insecurities right from the very start.