I must admit to being rather surprised at seeing these two characters juxtaposed in a question like this. This is because I don't think there are really many similarities between them at all, and what defines them in relation to each other is their profound difference. If we think about it, perhaps it would be more apt to compare a character like Lady Macbeth to Cassius, for it is Lady Macbeth who plays the role of temptress to her husband, just as surely as Cassius tempts Brutus.
It is Lady Macbeth who commits herself, body and soul, to the cause of making her husband king, and uses every resource that is at her command to ensure that this becomes reality. She is the one who browbeats and cajoles her husband into killing Duncan, even going as far herself as to make the plan and then finish putting it into action, smearing the sleeping grooms with Duncan's blood because her husband finds he is unable to do it. She is the character who shows strength and determination that is not impacted by the reality of murder--until the end of the play.
Brutus, on the other hand, is presented as a man whose devotion to the concept of honour is his definining characteristic. This is something that Cassius exploits greatly to his advantage, as he argues that Brutus would be honourable to join the conspirators, but throughout the play, Brutus continues to view himself and to try to be a man who is ruled by integrity and honesty. Of course, whether Brutus is in fact blind to his own ambition and the way that power clouds his judgement is another matter. He does play a part in the assassination of Caesar, but he believes he is doing it for the "right" reasons, and goes to the grave with these principles in tact.
Both Brutus and Lady Macbeth are responsible for the murder of a leader. Lady Macbeth plots the demise of Duncan, and Brutus is one of the many conspirators that stab Caesar. They both are able to disguise their true intentions in order to prevent their victim from becoming suspicious. Additionally, both Brutus and Lady Macbeth are faced with a great deal of guilt following their deed and as a result have "visions" that are indicative of their remorse. Lady Macbeth sees blood on her hands and Brutus sees the Ghost of Caesar.
Lady Macbeth and Brutus differ in their motivation and rationale for the murder. Lady Macbeth planned Duncan's assassination in order to seize power. Brutus participated in the conspiracy because he felt that he was acting for the good of Rome. Lady Macbeth was the ring-leader of Duncan's murder and goaded Macbeth into action. Brutus, on the other hand, was the one who was manipulated. Cassius played on Brutus' weaknesses in order to convince him to assassinate Caesar.