How did Antony and Caeser develop throughout the play?

Mark Antony gradually succumbs to the ostentatious luxury of Egypt and the seductive allure of its beautiful queen, Cleopatra. In doing so, he earns the contempt of many of his fellow Romans. Noble Roman warriors are supposed to be hard, manly, and spartan. They're not supposed to throw themselves into lives of unabashed indulgence and allow themselves to be ruled by women, least of all foreign women. Yet that is precisely what Mark Antony does, and in the process becomes somehow less Roman as a consequence.
Octavius, on the other hand, likes to portray himself as an unstinting champion of Roman values. He manipulates traditional Roman xenophobia and misogyny to paint an unflattering portrait of Mark Antony as a kept man who's sold his soul for a life of ease and luxury. Octavius doesn't really change throughout the course of the play, and this is undoubtedly one of his great strengths. Unlike Mark Antony, he hasn't been distracted from his single-minded goal of consolidating his power at Rome. He can therefore turn all his attention to defeating his former colleague and his Egyptian queen.

There are several differences between Marc Antony and Octavius Caesar as they change through William Shakespeare's play. The main difference is that at the end Antony dies and Octavius lives.
Octavius probably changes less because he resolutely pursues his ambition to be sole leader of Rome rather than one triumvir. He understands the need for combined strategy and military might. He almost loses by underestimating Cleopatra, but comes out all right. He pays tribute to Antony as a hero despite his lapses.
Antony seems to be in over his head. Trusted with command of the western areas and aiming to rule Egypt as well, he allows himself to get sidelined by his affair with the Queen of the Nile. His weakness for love and beauty prove his undoing. When he has the chance to strengthen the empire and solidify his own position by marrying Octavia, Caesar's sister, he does so—but then betrays them both. Hearing that Cleopatra is dead, he kills himself. However, she is still alive, so he gets to join his love one last time before they both die.