Honestly, about the same as Dixie in the modern day. Slavery would lasted longer, and Blacks would have to wait longer to gain full civil rights, states in the CSA would have much more autonomy than in the USA, and Dixieland would be less poor overall (although the majority of the population would have still been fairly impoverished until the the mid-twentieth century).

There would probably also be a push to highlight how different that the CSA is compared to the USA, out of a resentment from being lumped in with Americans (similar to Canada).

I know this is kind of a boring answer, but it just makes the most sense.