Can you compare and contrast Hamlet's character to other character in the play? What would you do if you were in Hamlet's situation?
Sure. If you wanted to take a really ambitious (and kind of tough) route, you could compare Hamlet and Fortinbras. That's a tough-ish one because even though they are both princes, and both lost fathers recently, Fortinbras isn't onstage much, so you don't have much to work with.
Better, perhaps, to compare someone you have more material on. How about Hamlet and Laertes? After Laertes' father Polonius is killed, no ghost has to show up to tell him what to do. Instead, he immediately starts to move for revenge, and within an act or so, he's dueling Hamlet. Sure, they both die, but think of how much better off Hamlet would have been if he'd skewered Claudius that fast.