The moment Anthony gets control of Egypt (and manages to hold it), he would have a huge advantage. He could play the populist and give free grain in Rome, since Egypt was still at the time the main supplier of food to Rome (this is the reason that made the Romans annex it in the end, since they were rather tired of having to keep the peace every few years in Egypt from feuding monarchs...). By subverting Octavian's base, it would become a lot more difficult for him to achieve a victory, and you have to keep in mind, despite being the loser in the end, Anthony was the better general between the two, and he would most likely win in a prolonged war.