What are the similarities and differences of the characters Brutus and Cassius?

There are more differences than similarities between the characters of Brutus and Cassius. The two men are similar in being courageous warriors, distinguished Romans, and in both being opposed to the obviously dangerous monarchical ambitions of Julius Caesar. Since Brutus and Cassius are the most important characters in the play, Shakespeare evidently wanted to distinguish them by highlighting their differences. Cassius is selfish, envious, and greedy. He is worldly wise and cunning. He is more outgoing than Brutus. He understands people far better than Brutus because he judges others by himself--and there are always more people like Cassius than like Brutus.
Brutus is a loner, a book-lover, a philosopher. He is moved by ideals rather than by personal interests. Like Cassius, he judges others by himself and consequently makes bad mistakes, most notably by sparing Antony's life and giving him permission to speak at Caesar's funeral. Brutus is kind, generous, and patriotic. He and Cassius are mismatched as partners and were bound to have serious problems in governing together, as dramatized in their famous quarrel in Brutus' tent in Act 4, Scene 2. Brutus only became involved in Cassius' plot to assassinate Caesar because he mistakenly believed Cassius to be noble, patriotic, and altruistic--like himself. 
Brutus is obviously a much better man than Cassius. Even Brutus' enemy Marc Antony pays him tribute at the end of the play when Antony and Octavius are viewing Brutus' dead body on the battlefield at Philippi.

ANTONYThis was the noblest Roman of them all.All the conspirators, save only he,Did that they did in envy of great Caesar;He only, in a general honest thoughtAnd common good to all, made one of them.His life was gentle, and the elementsSo mix'd in him that Nature might stand upAnd say to all the world, “This was a man!”