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.
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.