Caesar and Brutus share several personality traits and attributes. Both men are esteemed politicians who are respected by their peers and revered by the public. They are also powerful, influential men and play an important role in Rome's political arena. Caesar entertains the possibility of becoming emperor, while Brutus is known as an intelligent, prominent politician. Caesar and Brutus also admire and respect each other. Caesar trusts Brutus, and Brutus finds it difficult to assassinate his close friend.

Both men are also capable and ambitious. Caesar is accomplished on the battlefield and desires to disband the Republic in order to become emperor. Brutus demonstrates his ambition by leading the conspirators and carrying out the assassination. Similar to Caesar, Brutus seizes an opportunity and takes matters into his own hands to change the course of history. Caesar and Brutus are also risk-takers and make costly mistakes. Caesar makes the mistake of traveling to the Senate, where he is brutally murdered, and Brutus allows Antony to live, which has disastrous results.

Despite their similarities, Caesar and Brutus have entirely different personalities and goals. Caesar is a selfish, arrogant man and views himself as superior to others. Caesar is also focused on his political career and concerned about usurping power. In contrast, Brutus is a mild-mannered, humble individual who is selflessly concerned about the Roman population.

The only reason Brutus chooses to murder Caesar is to preserve the Republic and protect the citizens from a possible tyrant. Unlike Caesar, Brutus is inexperienced in political matters and naively believes that Cassius shares his concern for the people. Brutus lacks Caesar's shrewd, keen nature and trusts greedy politicians like Cassius.

Caesar is a man of action, while Brutus is an intellectual. Caesar is an extrovert. We never see him when he is not with someone else, and often he is surrounded by people, as he is at the time of his assassination. On the other hand, Brutus is often alone. He is an introvert. Even his wife Portia complains that he does not spend much time with her and refuses to confide in her. Caesar is ambitious. Brutus is not ambitious. Brutus seems happiest when he is able to read a book in private or just to meditate. Caesar likes Brutus, probably because Brutus is so different that their personalities complement each other's. Caesar also knows he can trust Brutus because of Brutus' noble character, and they are on the same level intellectually. Both men are superior to the men around them, and they both know it. This makes both of them seem egotistical, although both are smart enough to be courteous to everyone they deal with. Both men are highly respected for their strong characters. Brutus, like Antony, stands in Caesar's shadow. Both Brutus and Antony start to change when Caesar is eliminated. Both become more self-reliant, self-assertive, opinionated, domineering. The changes that take place in these two characters are among the most interesting aspects of Shakespeare's play. Antony makes a good leader, but Brutus does not. Brutus is too introverted, too bookish to be a strong, popular and successful leader. Antony has been a companion and protege of Caesar for many years; as a result he has absorbed a lot of Caesar's military and political wisdom. In the meantime, Brutus has been studying philosophy. Philosophers are not good teachers when it comes to practical matters. Caesar and Antony are "street smart," while Brutus is "book smart." Cassius is more like Caesar and Antony than he is like his partner Brutus. 

Caesar and Brutus are both important men, in positions of honour; they are political leaders who are respected and looked up to, and they are also close friends. By the start of the play, however, Caesar has already supplanted Brutus in terms of power and position and has, indeed, become the single most powerful man in Rome. 

The two men are notably different in character and outlook. Caesar is egoistic; he refers to himself grandly in the third person and is rather arrogant in his attitude towards others. Brutus, on the other hand, is very courteous and kindly towards others in his manner. Even more, he is concerned for others in political terms; he wants to preserve the Roman republic, where no one man can be allowed to amass supreme power, like Caesar. Whereas Caesar appears something of a political opportunist, seizing the chance for personal gain, Brutus is politically idealistic and acts for the greater good of Rome, not for himself. It is true that Caesar is seen to benefit the people of Rome in his will, but he does not at any time appear to care for the people in a political sense, as Brutus does.

Therefore, the two men differ considerably in their political opinions, actions, and general attitude towards others. Tragically, Brutus ends up feeling compelled to kill his old friend for the sake of his political idealism (which also marks him out as naive). He wrestles with his conscience over the matter:

It must be by his death: and for my part, 
I know no personal cause to spurn at him, 
But for the general. (II.i.10-12)

Brutus, then, is forced to admit that he has no 'personal' reason for killing Caesar at all, only his own belief that he has to act for the 'general' good, in a purely abstract sense. In the event, the ordinary citizens of Rome, in whose name he acts, prove themselves incapable of understanding his motives and turn against him and the other conspirators.

"Julius Caesar" is currently undergoing a bit of a critical reappreciation and - as you'll see if you look at other JC Q&As on enotes - there's a lot of argument about the play. So first point is that it depends on how you read the play.

But - for my money - the two are actually very similar characters. Antony says Brutus was "Caesar's angel", and that Caesar loved Brutus dearly (in fact, in some of the sources of the play, Brutus is Caesar's son!). They have a close relationship, it seems, and it is Brutus' betrayal which horrifies Caesar most ("Et tu Brute?" famously expresses shock that even Brutus is part of the conspiracy).

Both men spend most of the play referring to themselves in the third person, a habit not really shared by other characters in the play, and one which underlines their arrogance. As Cassius says

Brutus, and Caesar: what should be in that Caesar?
Why should that name be sounded more than yours?

Brutus is dragged into the conspiracy by an appeal to his arrogance and honour - and even he, idealistically, claims "not because I loved Caesar less, but that I loved Rome more". Caesar's arrogance leads him to think that he's invincible, and he goes to the Capitol, refusing to send an excuse.

Both men get key decisions wrong. Both men are idealistic and arrogant. Both men - in Shakespeare's play - end up dead.