This has to be one of the best fighting games I've ever played, partly because of the anime style of the characters and backdrops and mostly because of how fluent the controls are. They might take a while to get used to, but when you do you'll be pulling of massive 25-hit combos with ease.
The characters themselves are unique, including a ninja using a giant nail for a weapon and a half-cat half-human who loves to eat. The anime style is great, the sprites for each character looks amazing especailly in HD and the background for each arena is equally impressive.
There is a story mode for each character which you'll have to play through multiple times to get 100 percent for them, the story is really hit or miss but I found it fun, mainly because of the sharp writing some of them deliver.
If you go for the limited edition then you get an instructional DVD, which you'll probably want to watch if you are struggling a bit, and also an artbook. Unfortunately I don't think its as big as the American artbook but its still very cool. And all of this comes in a biggish cardboard box with the BlazBlue logo on the front and it looks great.
Basically if you enjoy your fighting games then you can't do much better than BlazBlue.