"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.