In To Kill a Mockingbird by Harper Lee, there are several elements that create a sharp contrast between Atticus and Aunt Alexandra.
First of all, Atticus is a man of few words. He does not socialize with people, though he is always polite and interested when speaking to others.
On the other hand, Aunt Alexandra is very sociable. She entertains women in various groups, and joins other groups. She has visitors over on a regular basis.
Atticus raises his children with intelligence, patience, good humor and flexibility. He leads by example, lets his conscience guide him rather than popular opinion, and recognizes the need for his children to see the world around them as it truly is rather than shielding them with ignorance. (We see this when he allows the children to know what is involved with Tom Robinson's case; Aunt Alexandra does not agree.)
Aunt Alexandra is concerned with appearances. Dressing correctly and acting in an appropriate fashion (especially with Scout wearing overalls instead of dresses) are very important details with Aunt Alexandra.
Lastly, Atticus does not have the same sense of familial history that Aunt Alexandra does. The children know stories of family members that their aunt would prefer they did not know; Aunt Alexandra's sense of family is not the same. Atticus is firmly rooted in his community, but is looking forward, hoping that Maycomb will be able to step out of the past and grow in a positive way.
For Aunt Alexandra the past is very important, especially the past of the Finches, a family which has been in the area for many years (as was introduced at the beginning of the novel). She is a genteel southern woman, and this can be seen in how she handles herself within the community. She is concerned that the children will have to sense of what it means to be a Finch, and even speaks to Atticus so he will talk to them.
Whereas Aunt Alexandra is concerned with appearances, Atticus is not, and will not allow himself, once again, to act in a way that does not follow his internal moral/ethical compass. Aunt Alexandra sins are more of omission: not telling the "whole truth," not recognizing the world as it truly is in order to maintain appearances.
Though they are brother and sister, Atticus and Aunt Alexandra are very different people.