I must admit I have not seen the anime but I believe, that the beginning of the series are more-or-less the same. However the anime is complete story, while manga is still not over (I wonder if they even intend to finish it, they managed to release Chobits and XXXHolic in meantime.. ). As far as I know it was not CLAMP that produced the anime series and the final episodes are based on assumptions of anime producers. The ‘real’ (that is intended by CLAMP) ending of the story is yet unknown.
I have also seen the animated movie (which is also based on assumption how will the story end) and it was more-or-less similar to manga, yet due to obvious reasons its much different – its only a story of Kamui and Fuma and the other chars are irrelevant. They appear fast, and die even faster. It is quite spectacular, but lacks very much in the plot.
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