Both Hamlet and Laertes do experience character growth in Shakespeare's Hamlet. Of course, as defines the tragic hero, Hamlet must experience self-knowledge and an increase in wisdom. Interestingly, it is in the graveyard scene in which Hamlet disentangles himself from his urge to kill Claudius out of vengeful passion and instead act for the sake of pure justice and rid Denmark of its corrupt court. It is with this disentanglement of his passions and his clear view of justice that Hamlet asserts himself and his sense of purpose, "This is I, Hamlet the Dane" (5.1.227).
With this new realization, Hamlet tells Horatio, "There's a divinity that shapes our ends," and concludes,
Does it not, think thee, stand me now upon—
He that hath kill'd my king, and whored my mother;
Popp'd in between the election and my hopes;
Thrown out his angle for my proper life,
And with such cozenage—is't not perfect conscience
To quit him with this arm? And is't not to be damn'd
To let this canker of our nature come
In further evil?(5.2.68-75)
Reckless in judgment and bold, Laertes is the antithesis of Hamlet. After returning from France, he is immediately ready to kill Hamlet in order to avenge his father's death without investigating what has precipitated this death. He rashly judges Hamlet and is ready to duel him in the graveyard when he discovers that his sister Ophelia has died. Then, he impetuously contracts with Claudius in a dishonorable plan to slay Hamlet with poisoned rapier and drink. Even when Hamlet makes apologies, Laertes accepts them only "in nature," withholding complete reconciliation. However, as they duel, Laertes realizes the wrong that he does Hamlet as he tells Claudius that he will strike Hamlet, saying, "And yet it is almost against my conscience" (5.2.301). And, it is his conscience that overtakes Laertes passion as, dying, he admits the evil of Claudius and begs forgiveness of Hamlet:
He [Claudius] is justly served.
It is a poison temper'd by himself.
Exchange forgiveness with me, noble Hamlet.
Mine and my father's death come not upon thee,
Nor thine on me! (5.2.335-339)
Unlike Hamlet, who is both admirable and successful in his defeat as he attains self-knowledge and rids Denmark of its corruption by passing the crown to the noble Fortinbras, Laertes dies in disrepute; nevertheless, he does possess an honorable conscience and demonstrates self-knowledge in asking forgiveness at the play's end.