On the surface, the two couldn't be more different. Aunt Alexandra is horrified that Scout likes to wear pants and just doesn't act properly in so many ways. Aunt Alexandra is all about custom and maintaining a certain image and doing everything right in terms of other people's opinions.
But underneath it all, both Scout and Aunt Alexandra are willing to recognize hypocrisy and to challenge some things when they are really pushed into a corner. For Scout it happens more often, perhaps because she is more of an impetuous child, but Aunt Alexandra also shows her willingness to do so when she stands up to her missionary group by calling them out on their hypocritical attitude towards the black members of their town and the people they are trying to "save" in Africa.
Scout doesn't enjoy wearing dresses and doesn't think that she has to. Aunt Alexandra is very traditional and believes that woman should wear dresses, hats, and host parties where other traditional women gossip about people. Aunt Alexandra is prejudice and doesn't like the fact that Cal is the cook, simply because she's black. Scout doesn't know racism. Aunt Alexandra believes that Scout needs a woman around to show her womanly ways, whereas Scout doesn't think that it's ness to have a mother since she has such a great dad.