Aunt Alexandra and Miss Maudie are roughly the same age and grew up as neighbors at Finch's Landing. But for all the background these women share, they couldn't be more opposite. Lee uses the contrasts between these two characters to further delineate the theme of tolerance in To Kill a Mockingbird.
Aunt Alexandra is very conscious of Maycomb's social mores, chooses to live within its constrictions, and "given the slightest chance she would exercise her royal prerogative: she would arrange, advise, caution, and warn." Even her clothing is tight and restrictive. Miss Maudie, on the other hand, sets herself toward the outside of Maycomb's conventionality. Like Atticus, she stays within bounds, but follows her own code.
Although Miss Maudie is quick to welcome Aunt Alexandra as her new neighbor, she's also quick to take her to task. When Aunt Alexandra states, "'I can't say I approve of everything he does, Maudie, but he's my brother,'" Miss Maudie reminds her that Atticus is doing a wonderful thing and that many in the town support him, even if that support is quiet. Aunt Alexandra is also extremely critical of Atticus' parenting style, while Miss Maudie is much more sympathetic. But then, Miss Maudie has a delightful sense of humor, a trait Aunt Alexandra does not possess.
Aunt Alexandra works hard at being feminine, but Miss Maudie doesn't seem to care about those things. She wears men's overalls when she works in the garden, but is equally comfortable in more traditional garb. Aunt Alexandra has a personal quest to make Scout "behave like a sunbeam," but Miss Maudie accepts her as she is. Consequently, Scout finds in Miss Maudie a kindred spirit who helps her make sense of being female and, with Atticus, helps Scout develop tolerance. Miss Maudie treats the children in an adult manner, much like Atticus does. She never laughs at Scout's mistakes and she trusts the children to play in her yard within the boundaries she's set for them. Aunt Alexandra is "analogous to Mount Everest: . . . cold and there" while Miss Maudie is warm enough to pop out her dentures for Scout to see.
Miss Maudie has a quiet spirituality that shows itself only when taunted by "'the foot-washers [who] think women are a sin by definition.'" Aunt Alexandra displays her beliefs much more publicly. She's active in the Missionary Society, which appears to be as much a social club as a religious organization. Tolerance isn't a big part of the Missionary Society meetings, either. The ladies' lamentations over the living conditions of the Mrunas, an African tribe, leads to a discussion about how ungrateful the women believe Maycomb's African American community to be. Miss Maudie is the person who ends that line of conversation with two sentences. Aunt Alexandra may not always agree with the course of discussion, but she refuses to be confrontational outside of her own family.