Starting with your idea of their fathers - think beyond just the relationship each girl has with her father. Think about the relationship each girl has with her family*. Scout's is decidedly better, more loving, closer, and more accepting.
* I think you could also make a pretty extensive list of personality differences as a result of the girls' family situations. They are exactly as obvious as you would think.
Also, they have a pretty distinct age difference. Scout is just starting the 1st grade - Lily is 13 or 14 when the story opens. *This is an ironic difference as the perspectives sound as if the girls could be peers.
There is also a difference in the education of each girl. Both receive an education as a result of experience, but Scout's education is decidedly more formal. It is influenced by reading, academic discussion, and being surrounded by educated adults. Lily on the other hand is clearly experiencing a new kind of education - but hers is more of a hands-on, rural experience. The time she spends at August's house is valuable in a different way than books and academic discussion. She is experiencing a new way of living, directly. This cannot be ignored as part of her education.
There is a difference in the time-period of each book as well. Mockingbird is set in the time of the great depression. Sure, no slavery - but this is during the time of accute segregation, Jim Crow laws, and a major lack of racial equality as a way of life. Lily lives in the 1960s - right in the heart of the Civil Rights Movement. While racial tensions are still high and equality is still relatively low - the racism Lily experiences is more controversial on a global level. Whereas the majority of Scout's world doesn't even consider "racism" to be wrong yet - Lily lives in a time when this debate was raging, Black America was gaining a voice of its own, and there was the beginning of support from whites for this advancement. To put it simply, Atticus Finch would not have been in such a minority had had his story been set in the 60s.