Despite the fact that Hamlet and Laertes end up in a deadly duel by the end of Hamlet by William Shakespeare, the two men have many significant points of comparison.
First of all, in Act I scene ii both Hamlet and Laertes would rather be somewhere other than Denmark. They are both students, and they both want to return to school. While Laertes gets permission from Polonius to leave, however, Hamlet is asked by his mother and stepfather to stay. This is a warning to readers that "something rotten" is ahead for Denmark.
Second, both Hamlet and Laertes purpose to avenge their fathers' deaths. Hamlet wants to kill Claudius and nearly does in Act III scene iii:
Now might I do it pat, now he is praying;
And now I'll do't. And so he goes to heaven;
And so am I revenged. That would be scann'd:
A villain kills my father; and for that,
I, his sole son, do this same villain send
Eventually, in the moments before he dies, Hamlet does kill Claudius. Laertes wants to kill Hamlet (because he killed Polonius) and does, though he asks forgiveness for it once he realizes that Claudius has used him to kill Hamlet.
Both Hamlet and Laertes plot and scheme, the former to reveal Claudius's guilt and the latter to kill Hamlet (with Claudius's prodding, of course).
Hamlet and Laertes both love Ophelia, though certainly their love for her is not the same. Hamlet does seem to love Ophelia, despite his actions and protestations to the contrary (probably as part of his plan to kill Claudius as well as his attempt to protect her). Laertes gives his sister some advice about loving Hamlet (to protect her) before he returns to school, and when she does he is so distraught that he jumps into the grave with her casket. Act IV scene i is the first time the two men cross paths directly, and they are virtually the same. Both men protest their love for Ophelia as the stand in her grave, and they are certainly more alike than different as they do so.
Both men have good reputations and are beloved, Hamlet by the people of Denmark and Laertes by his schoolmates. Though Hamlet acts slowly (almost painfully slowly) throughout most of the play, he acts quickly and decisively in his last moments of life. Laertes is more rash from the beginning, but the two men are well matched in terms of their quick action at the end of the play.
In general, both men are interested in the same things for most of the play: they love Ophelia, they want to protect her, they love their fathers, and they want to avenge their fathers' deaths. To think of Hamlet and Laertes as mirror images (though not exact) is fair and even necessary.