"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.
Caesar, the title character of William Shakespeare's play "Julius Caesar," and Brutus are both incredibly rich, expertly drawn characters for a play that has everything for everyone.
Caesar is portrayed as a physically weak but shrewd politician. Caesar refuses to be crowned emperor three times to demonstrate that he is unambitious, but in his position, he didn't feel he had to accept a crown as he was already "the man in charge."
Caesar is also physically weaker. He suffers from seizures and during the swimming match with Cassius, he cries,"Help me, Cassius or I sink" (i.2.12). When his wife tries to persuade him not to go the senate because of her premonition, Caesar wavering between magic and his own ego, decides to go anyway.
Brutus is motivated by his love of country, rather than self. He does not act out of selfish reasons but believes his actions will make Rome stronger. Both men are loved by the citizenry.
Caesar is then assassinated, and later Brutus commits suicide. A fitting end for both characters as they put their trust in the wrong people. Brutus puts his trust in Cassius, and ends up ruined, Caesar puts his trust in himself and doesn't realize people will rise against him.