In Shakespeare's Julius Caesar, these three characters are very different. Although the play is called Julius Caesar, it is more about Brutus who is our tragic hero.
Julius Caesar is a great military strategist, leader, fighter, and is beloved by many. He has become the head of the Roman Empire, and there is talk of making him a "king." Some of the information we get about Caeser comes from other characters, a common technique in literature, called direct characterization. When coming from other characters, however, this information can be suspect, based on their personal biases, either in a negative or positive way.
For instance, Cassius hates Caesar because he once saved Caesar from drowning, but now has to bow when Caesar passes like any other lowly subject, so it is hard for us to trust what Cassius says of Caesar.
However, Brutus, after murdering Caesar, speaks of his leader's greatness, but also his ambition:
Romans, countrymen, and lovers! Hear me for my cause...
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. If then that friend demand why Brutus rose against Caesar, this is my answer: 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 freemen? As Caesar loved me, I weep for him; as he was fortunate, I rejoice at it; as he was valiant, I honor him; but as he was ambitious, I slew him. (III.ii.15, 19-28)
Brutus sees Caesar as one who who enslave his people under the title of "king," and Brutus loves Rome to much to allow this to happen, which gives us Brutus' perceptions of who he is.
Cassius describes Brutus (to Brutus), and may well speak for many Romans, though we also know he is trying to turn Brutus against Caesar; but Brutus is an honorable man who loves Rome more than himself. Cassius says:
And it is very much lamented, Brutus,
That you have no such mirrors as will turn
Your hidden worthiness into your eye
That you might see your shadow. I have heard
Where many of the best respect in Rome,
Except immortal Caesar, speaking of Brutus... (I.ii.60-65)
Mark Antony may seem like a good man, and the person to follow in Caesar's footsteps, but in some ways, he is just as ambitious, if not more, than Caesar. When Brutus admits to killing Caesar, he asks Antony to let him explain his actions to the people. Antony allows this, insinuating to Brutus and the others that he will not judge them. However, after the crowd accepts Brutus' reasoning, Antony speaks to the crowd and turns them against Brutus using rhetorical questions—Brutus, a good man, says Caesar was ambitious...are these things he did ambitious, and wrong?
...Brutus says he was ambitious,
And Brutus is an honorable man.
He hath brought many captives home to Rome,
Whose ransoms did the general coffers fill.
Did this in Caesar seem ambitious?
When that the poor have cried, Caesar hath wept;
Ambition should be made of sterner stuff.
Yet Brutus says he was ambitious,
And Brutus is an honorable man.
You all did see that on the Lupercal
I thrice presented him a kingly crown,
Which he did thrice refuse. Was this ambition? (III.ii.04-105)
By making these points, Antony infers that Brutus is dishonorable; he also infers that Caesar was great. In doing this, we learn that Antony is not above giving his word to men and turning the situation to his advantage when it suits him.