This will be a look at the personalities I see them having.
Ancient Greece's personality was shaped by the attitudes of her people. Many expected her to be quiet and let the male nations to make all of the choices. This lead her to become even more outspoken to get someone to listen to her. Most of the time, it's her way or the highway.
Ancient Egypt is more of a foil to her friend. She's calmer and less likely to speak out. Many times, she strives to find compromises to benefit both parties.