The most obvious similarity between Brutus and Cassius is the fact that they both want to be rid of Caesar, albeit for different reasons. Furthermore, both are respected senators and have garnered much honor for their bravery. It is obvious that each of the two men deserve their status. Both of them have a following and are much admired by those they lead.
The main contrast between the two men lies in their different ambitions. Cassius' desires are clearly self-serving, while Brutus cares more about Rome than his aspirations. Caesar himself comments about Cassius having a "lean and hungry look" in Act l:
Yond Cassius has a lean and hungry look;
He thinks too much: such men are dangerous.
When Brutus addresses the citizens after Caesar's murder, he makes the reason for the assassination clear.
Not that I loved Caesar less, but that I loved
Rome more. Had you rather Caesar were living and
die all slaves, than that Caesar were dead, to live
all free men?
Furthermore, Cassius is clearly jealous of Caesar and is bitter of the position the general has attained. He consistently reminds Brutus about Caesar's weaknesses and cannot understand why he has to receive such praise and admiration when, as Cassius believes, he is a weakling and a coward. Cassius is resentful of the fact that he and others should bow to the authority of one so feeble and inept.
Brutus, conversely, has only love for his leader. He states as much in his address to the crowd:
If there be any in this assembly, any dear friend of
Caesar's, to him I say, that Brutus' love to Caesar
was no less than his.
Brutus' only fear is that Caesar might become a tyrant and harm Rome if he should gain too much authority. He is afraid that, as emperor, Caesar would enslave them all. His fear of oppression is the reason he gives for Caesar's assassination.
Cassius, unlike Brutus, is also sly and manipulative. It is easy to see how he manipulates Brutus by consistently commenting on his noble character and his courage. His flattery has a hidden purpose—he wants Brutus to join his scheme. To further this end, he asks Cinna to plant letters urging Brutus to become involved in the conspiracy to rid Rome of Caesar.
Brutus, unlike Cassius, is quite naive and does not, for example, see any danger in allowing Antony to address the multitude. When he decides to give Antony permission to speak to the citizens, Cassius tells him:
You know not what you do: do not consent
That Antony speak in his funeral:
Know you how much the people may be moved
By that which he will utter?
Brutus, however, ignores his warning and, to their fatal detriment, allows Antony to speak at Caesar's funeral. It is this belief in the virtue of others that also separates the two men. Brutus is somewhat gullible while Cassius is sly, scheming and sees only the worst in others. Brutus is noble and honorable while Cassius is insidious.
In the end, it is a combination of Cassius' ruthless ambition and Brutus' lack of guile and his innocent belief in the good of others that brings about their destruction.
Brutus and Cassius are both quite ambitious. I would say that is where their similarities stop. Cassius is manipulative and is motivated by his own desires for power. Brutus, however, truly wants what is best for Rome and thinks carefully about any of his actions to be sure that what he is doing is for the good of the Roman people.
For an in-depth answer, this would be a very good question for the Enotes Q&A section. Briefly, they are alike in their desire to be free of the potential tyranny of Caesar. They differ in how they approach the problem of Caesar. Cassius is willing to resort to any tactics to get what he wants. Brutus always wants to do things in an honorable and noble manner.
i must agree with mwalter822 -- both Cassius and Brutus wish to rid rome of Caesar (i.e. dictatorship) -- but Cassius is personally ambitious too and harbours a sense of envy against Caesar's meteoric rise, whereas Brutus is purely idealistic. It is not that he 'loves Caesar less', but that he 'loves Rome more'.