The biggest downside to Valkyria Chronicles II is that it doesn't quite have the same charm as the original when it comes to the story and characters. That's not to say the original was a masterpiece of narrative (it definitely wasn't), but VCII goes overboard with the anime clichés and high school drama angle, making it feel a lot more generic than the first.
Luckily, most of the insipid school drama is skippable, since you have to choose to watch it by selecting to watch events from the overmap, and there's no penalty for only watching main storyline scenes. And even without all the optional cutscenes, there's still more than enough content (over 200 battles!) to sink tons of hours into.