Not at its Best
I have to say that I'm a little surprised to see all the 5-star reviews for this game.
I am a huge Hakuouki fan; I own all the games in this series, usually on multiple platforms.
That said, I think this game is probably the least exciting game in the series.
This game is built on a "what-if" storyline, where the developers claim (or disclaim) to take liberty with historical events to create a world of its own. I have no problem with that. I do like my history, but I wouldn't dream of looking for historical accuracy in a video game.
To me, that disclaimer meant the developers had a free pass to create a whole new storyline and do whatever they wanted with these interesting characters they've spent so many games in developing. Unfortunately, that is not what happened.
The story is weak and not very interesting, nor is there is any new character development. It seemed they wanted to keep enough "truth" to the historical events to keep the history buffs interested, with the end result being that they annoyed made the story just annoying enough - kinda like nails on a chalkboard.
In my opinion, they should have just gone all out instead of trying to tweak real events in an unreal way.
As for the action part of this game, this game, dare I say it, bored me so much that I had to put my PSP down after each scene because I just...I was so BORED!!
I finished the game (as an avid Hakuouki fan, not completing the game was not an option) but I think you would have to be a real die-hard fan (like me) to be able to do this. This game on its own really has very little to offer (I hate to say it).
I have a tendency to re-play games, but I doubt this game will get another play now that I've completed it.
In sum,
If you are looking for a good action game, go for the original "musou" series that Koei offers (that is the system this game is based off of).
If you are looking for a good novel game (with a little bit of romance), go for the original Hakuouki game.
If you enjoy the original Hakuouki game and feel like you want to play every game in the Hakuouki series, then, and only then, I would tell you to try this game.
Japan 
