At the opening of the scene, Brutus is frightened to state his wishes out loud — perhaps ashamed to state his desire to die out loud because he is denying his lifetime philosophy, stoicism, which precludes suicide. This shame would have been prevalent in an Elizabethan audience, to whom the act of suicide would be abhorrent. Still, by running on his sword (note the difference between his death and that of and Cassius, who has Pindarus run the sword through him), Brutus is heroic. To Shakespeare's audience, he would have been a classical, sympathetic, tragic hero, ready to die rather than be conquered. In addition, with a slight shift in perspective, he could also be a Christian hero, sacrificing his life as a result of his decision to fight for the good of the people. (Audiences in Shakespeare's time expected to be able to get more than one meaning from what they saw in the theater and what they read on the page. It was part of the fun.)
In the final analysis, the narrative of both the Christian and the classical hero belong to Brutus and they belong to him because it is "Brutus' tongue" that defines and tells the story. Even though Antony and Octavius have the last word, their praises are, in fact, epilogue.
One addition: Note in Act V, Scene 5, the precariousness of the ending. Shakespeare's finales almost always leave room for doubt, and this play is no exception. Caesar's reputation as a great ruler may have been reclaimed, Cassius' cynical persuasion of the conspirators may have been converted into a great and noble friendship with Brutus, and Brutus' faults may have been glossed over, but despite all the changes effected in this drama, Julius Caesar ends as it began — with an uncertain future.
