There's another connection between Brutus and Hamlet: when the ghost of Caesar appears to Brutus in his military tent.
What are the differences? First of all, in Hamlet, the ghost appears to his possible avenger. In Julius Caesar, the ghost appears to his killer. Also, in Hamlet, Hamlet is not the first one to see the ghost, he is just one of several witnesses. In Brutus' case, however, he is the only one who sees or hears the ghost.