The funeral speeches in Act 3 contain numerous examples of both appeals.
Ethos (the speaker's establishing his or her credibility or an appeal to morals/values):
Examples: In Brutus's speech, he begins by addressing the crowd as "Romans, countrymen, and lovers," demonstrating that he is one of them and that he values their role in Roman society. This helps establish credibility, and as Brutus continues by arguing that he killed Caesar to protect all citizens from Caesar's ambition, he appeals to their sense of Roman values. Similarly, Antony employs a multitude of ethical appeals. Like Brutus, he groups himself with the crowd and addresses them as "Friends, Romans, and Countrymen." He also asks their permission to leave the platform and go down among them--this helps establish his credibility as "one of them," not as someone who is above them. While much of his speech appeals to the crowd's emotions (pathos), Antony does discuss the people's duty to Caesar by showing what a "people's" leader Caesar was.
Logos (an appeal to logic through the use of facts, statistics, etc.)
Examples: Brutus uses logos when he cites examples of Caesar being too ambitious and seeking a crown when the Romans had already suffered under the reign of a tyrant king. By bringing up elements of Roman history and true events involving Caesar, Brutus seeks to demonstrate that the assassination was a planned action based on thought and facts. Antony, too, employs logos when he lists examples of Caesar's actions on behalf of all Roman citizens--his willingness to share the spoils of war with the people and his establishing a reputation for Rome throughout the known world; even Brutus could not the truth in Antony's words. The will itself is another example of logos. While Antony uses the literal will to stir up the crowd's emotions, the contents of the will represent logical support for Antony's defense of Caesar. The will leaves the each citizen a stipend and land to use for public parks.
Hope this helps!
Concerning ethos and logos in Shakespeare's Julius Caesar, the honor the Roman leaders emphasize is an example of ethos. Ethos is a disposition, character, or attitude peculiar to a specific people or group.
Their form of honor is central to their worldview and self-image. Notice the emphasis on Brutus's honor throughout the play. When Antony's speech ironically exposes the behavior of Brutus and the other conspirators as dishonorable (though Brutus's motivations are honorable, his behavior isn't, and that's what is exposed by Antony), the mob riots. When Cassius and Brutus lose the battle, they both choose death instead of surrender or capture. When the battle is over, Antony picks out Brutus as the lone honorable conspirator.
Concerning Logos, I believe the omens in the play are an example of the order of Rome being disturbed. If logos is the source of world order and intelligibility, Rome, in the play, is out of order and unintelligible. The hand that burns, yet doesn't, and the lion loose in front of the capitol are signs that all is not well.