I think divergence in education and Southern cultural values contribute to the differences between Atticus and Alexandra.
Atticus, a lawyer, and his brother Jack, a doctor, were given more opportunities to succeed on their own, as opposed to Aunt Alexandra, who has defined herself more by social mores. Aunt Alexandra has bought into the Southern debutante culture, believing that women should fit into roles, as dainty ladies who wear formal dresses, attend social gatherings, and play coy with the men. Whereas Atticus lets Scout wear overalls and go shoeless, Alexandra wants her dolled up in gowns and hats.
Atticus, on the other hand, doesn't seem a part of the Southern male culture of honor. He doesn't buy into the Southern aristocracy class system which holds the white landowners privileged over all. Through a more liberal education, Atticus and Jack have been raised to be open-minded and independent.
In turn, Atticus raises his kids to fend for themselves. He doesn't act like more "dads," insisting his kids address him with no formalities ("sir") or nicknames ("daddy"). Instead, he is simply "Atticus," symbolic of his no frills parenting.