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Batman: Gotham Knight reminds me a lot of the Animatrix. Both have the same premise: different anime artists putting their spin on a pre-established franchise. I liked the Animatrix even though I didn't really like the Matrix movies. Something about them just didn't do it for me. Batman, however, is one of my favorite comic book heroes. So I really love seeing a new spin (or spins) on the character.
The animation is top-notch. You can tell that a big budget was alotted to this project. There are a lot of action sequences that are beautifully animated. Good stuff.
The only other experience I had of the Japanese perspective on Batman was that one level in Shinobi (or was it Revenge of Shinobi) where the bosses were Spider Man and Batman. Batman actually had bat wings and flew around the screen while trying to suck your blood. That was fucked up. Batman: Gotham Knight, however, is not fucked up. So far, it is damn good.