What are similarities between Julius Caesar and Brutus, and how do they lead to their downfalls?

Both Julius Caesar and Brutus are extremely proud men. This may be why they are such good friends. In Antony's funeral speech he says:

For Brutus, as you know, was Caesar's angel.
Judge, O you gods, how dearly Caesar loved him!     I.2

Caesar can be friends with an equally proud man because he knows that Brutus is a reclusive, scholarly type who would never become a competitor. Caesar hides his own pride from the populace by deliberately acting humble and modest. Brutus is a solitary type of man who is not ambitious either for riches, fame or power. Nevertheless, when he finds himself the leader of the conspiracy he becomes overbearing. He believes that only his own ideas have any value and insists on having them carried out. He is a kind, generous, trusting man, but he reveals his one fault of what might be called hubris continually. Even his agonizing over whether to participate in the conspiracy against Caesar displays his hubris. He seems to think everything depends on his decision. Notice how he speaks to Cassius in Act 1, Scene 2 and to the plebeians in Act 3, Scene 2.

That you do love me, I am nothing jealous;
What you would work me to, I have some aim.

Brutus' entire reply to Cassius is crammed with the words "I," "me," and "my." Brutus is a supreme egotist, just like his great friend Caesar. Here is a bit from Brutus' funeral speech after the assassination:

Believe me for mine honor, and have respect to mine honor, that you may believe. Censure me in your wisdom, and awake your senses, that you may the better judge.

Brutus' entire funeral speech is about himself and his honorable intentions. He permits Antony to follow him in addressing the plebeians because he is so sure of his charisma and eloquence that he thinks anything Antony might say will be overshadowed or negated by what he himself will say. Antony knew how to manipulate Brutus into getting his permission to speak at Caesar's funeral. He appealed to Brutus' self-image as a noble, benevolent man.

Brutus is a thinker and Caesar is a man of action, but both men are infatuated with themselves. Caesar is killed because his great pride inspires him to become the sole monarch of the Roman empire. His ambitions are too obvious and too inimical to the interests of too many others. Brutus' great pride is self-contained. He is an introvert. He likes solitary meditation and reading. But by keeping himself so much to himself, Brutus does not acquire the "street smarts," the worldly wisdom that is seen in Caesar, Cassius, and Antony. Therefore, Brutus makes many bad mistakes. Trusting Cassius is one mistake. Trusting Antony is another. Brutus should never have allowed Cassius to talk him into joining the conspiracy against Caesar in the first place. Even Cassius says ao:

Well, Brutus, thou art noble; yet, I see
Thy honorable metal may be wrought
From that it is disposed; therefore it is meet
That noble minds keep ever with their likes;
For who so firm that cannot be seduced? 
Caesar doth bear me hard, but he loves Brutus.
If I were Brutus now, and he were Cassius,
He should not humor me.          Act I, Scene 2