One of the most important things about Mary Chesnut's diary is that she looks at her region of the country through very critical eyes. She is willing, for example, to talk about how many white men have children with slave women and she is willing to talk about the "white trash" who were part of Southern society.
So, if she had been writing in the North, I would expect that she would have looked at all of its "warts" too. The diary, then, would have been different because it would have looked at Northern problems instead of Southern problems.
A Northern Mary Chesnut might, for example, have paid more attention to poor immigrants and to the problems faced by workers in the factories. She would have looked at these major social/economic problems instead of the ones that were more endemic to the South.
So the diary would have been the same, I think, in that it would have looked at social problems. But the nature of the social problems it looked at would have been different.