What an interesting question! The major differences between the two women are obvious. Of different races, they lived in different historical eras in different countries and occupied different levels in social stature: the wife of Rome's ruler and the housekeeper for a small-town Southern lawyer. Beyond these differences, however, lie some more subtle differences that relate to their characters and personalities.
Caesar's wife is fearful, superstitious, and easily intimidated. She is shaken by terrible dreams, believing that her husband's life is in mortal danger; she tries desperately to convince him to stay at home instead of going to the Senate (where he was indeed assassinated). Despite her overwhelming fear, however, she gives up her argument immediately when challenged by Caesar and the conspirators. She is essentially a weak woman. There is nothing weak, however, about Calpurnia (Cal) in To Kill a Mockingbird. She dominates the children's daily lives, caring for them and keeping them on the straight and narrow, despite their frequent and heated protests. Jem and Scout know there is no way around Cal when she has laid down the law. She will not be moved.
These two women are alike in this respect: Both exhibit great devotion to those they love. Calpurnia lives her life for Caesar, accompanying him and supporting him. Cal has stayed with Atticus since the death of his wife, making a home for him and his children, becoming far more to them all than a housekeeper. As Atticus explained to Alexandra, "She's a faithful member of this family . . . ."
Comparing the two Calpurnias also forces us to compare their men. Atticus and Julius Caesar are both upright servants of the people who are destined to lose despite their best efforts. Both ladies are responsible for raising children who belong to the men but are not their own. Education and democracy would be important to both. (Cal teaches Scout how to write, and her own son Zeebo how to read.)