I'm only on Chapter 10 of Nohr currently, so I can't say very much.
So far, there have been a couple different objectives: kill all enemy units, kill the boss, seize the point, and the one I'm currently on, defend for 11 turns (Chapter 10), which is kicking my ass.
Dragon's Vein adds a couple variations to how you play, but I haven't found it necessary to use so far (excluding one chapter where it was necessary). I'm still early in the game, so I haven't seen anything really special yet, but judging from the difficulty/design of Chapter 10, I'm expecting a lot more map variation in later chapters.