"Antebellum" - Latin for 'before' = "ante", Latin for 'war' = 'bellum" thus the phrase means 'before the war' or 'pre-war', in this case, specifically, the American Civil War.
It depends on the context. In some situations either expression may be used and will mean the same thing. It would be a matter of personal choice. But there are situations when one form is better...
The phrase "home sweet home" is overused and can be considered cliche. However, it is very true that there is no place like home and most people are happy there so the cliche is justified.