Hamlet is indecisive. This might be explained by Hamlet's apparently cautious nature and his need to be certain about a course of action before he takes it. But even after Hamlet is absolutely certain that Claudius murdered his father, and despite the fact that he swore to avenge his father's murder, he does nothing about it.
It's not until the end of the play that Hamlet appears to take revenge against Claudius, but Hamlet's killing of Claudius seems to be motivated by his immediate anger towards Claudius for causing his mother's death and for conspiring with Laertes to kill him rather than by a compelling need for revenge.
Had these events not occurred, how long would it have been before Hamlet actually avenged his father's death? Throughout the play, Hamlet does everything he can to avoid fulfilling his vow to his father's ghost. He has a perfect opportunity to kill...
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Claudius but rationalizes himself out of doing anything at all. Instead, Hamlet lashes out at everyone else around him, perhaps because he's angry with himself that he simply can't do what needs to be done.
Indecisiveness is not one of Othello's shortcomings. Othello is cautious, like Hamlet, but once Othello makes a decision, he takes deliberate action. Othello doesn't second-guess himself like Hamlet does. Whether he's breaking up a fight in the streets, leading an army in the field, or killing Desdemona, Othello sees a course of action, decides what to do, and does it.
Decisiveness is not a naturally tragic flaw in Othello; it is rather through the machinations of Iago that this trait is exploited. Ordinarily, Othello's decisiveness serves him well, but Iago uses Othello's decisiveness to work his evil through Othello's truly tragic flaw: his jealousy. Ordinarily, Othello is a calm and calculated man and who takes all evidence into account when making decisions. Othello's jealousy, however, causes him to abandon his strict standard of rationality and empirical data, and he lets Iago lead him down the path to Desdemona's and his own destruction.
Iago also exhibits this flaw of jealousy, which drives him to his own downfall. He's jealous of Othello, of Othello's marriage to Desdemona, and of Michael Cassio's advancement in Othello's esteem. Thus Iago decides to destroy all of them.
The difference between Othello and Iago is that Othello's jealousy arises from his intense love for Desdemona whereas Iago's jealousy arises from his intense hatred for just about everyone around him who Iago thinks has succeeded at his expense.
One of the major differences in the flaws of the two characters is that Hamlet is one who appears to be able to think clearly and see the problems around him and the falseness of Claudius, etc., but he lacks the ability to act on them. He bemoans his inability to make a decision, to the point of even pointing out his inability to kill himself.
Othello, on the other hand, is duped severely by Iago and is completely unable to see the innocence of Desdemona or the scheming of Iago as he builds the illusion of Desdemona cheating on him.
They are similar in that Hamlet, considered a daring and dashing and intelligent figure is completely inept when it comes to action and Othello, whose warlike nature and prowess on the battlefield are no match for for the "intrigue" of life without warfare. Both men are incapable of living up to their image.