No there isn't any new content with another class.
Let's use wow As an example.1 character to max lvl and clearing recent raid = beating the game ( sort off)
Now u start another character( ie class in ff) it's the same thing. Except in wow , you can take a different leveling route to your first character and mid it up( different content).
Ff only has 1 main linear way to level, grind the same fates in the same locAtion with the same people over and over , there's no variety at all. Sure , throw in a dungeon and hunting log, but it's all just the same .