Hamlet and Laertes have several differences, but the central one is that Laertes is more a man of action, while Hamlet is more of a thinker. This key difference is most obvious from their responses to the deaths of their fathers.
When Hamlet's father dies, there is at first a swirling of questions around his demise, but when the ghost of Hamlet's father demands revenge, Hamlet still wavers, waiting and waiting for just the right time to exact his vengeance on his uncle-turned-stepfather Claudius.
When Laertes' father dies, Laertes wastes no time seeking vengeance. He rushes into the palace with sword drawn, ready to kill the guilty party. Claudius turns this to his advantage, of course, making Laertes his ally in his plot to lure Hamlet to his death.
Another instance showing their differences involves Ophelia. Laertes sees things in black and white, and so, when Hamlet seduces Ophelia (Laertes' sister), causing her to fall in love with him, Laertes exudes a sense of discomfort, angered by the way his sister is being treated. Hamlet is passive-aggressive with his talk toward Ophelia, both before and after the seduction, and the end result is her own insanity. It is difficult to imagine the straight-as-an-arrow Laertes treating a woman in this way.