It's kind of hard to categorize this movie. There aren't very many musical horror/comedies; the only other one I can think of is Little Shop of Horrors. LSOH is more comedy than horror, while Sweeney Todd definitely leans much more in the horror direction. Plus, most things that Tim Burton does cannot be categorized with anything else.
I didn't know the source material going in; never saw or read the play, and never heard any of the music except when a friend sang a few lines from "The Ballad of Sweeney Todd." That was years ago and it wasn't even in the movie.
Anyway, I think I liked it. It was at least effective horror, in the sense that it creeped out and disgusted me, so I can't say I really ENJOYED watching it, but I appreciated the art direction. It also had very effective comedy moments, especially every scene that featured Sacha Baron Cohen. People who like seeing Alan Rickman as a villain will probably like his role here, although since he plays a contemptible pedophile, people who think Alan Rickman is sexy will probably not like the role.
Johnny Depp did an excellent job, and completely personified the "Magnificent Bastard" entry in TV tropes. One thing I've always liked about Johnny Depp is the way he plunges into a role. Whatever weird stuff you throw at him, he always plays it to the hilt. This movie is no different. Probably my favorite number was when Helena Bonham Carter sings her glurgy fantasy about how she hopes that they will live by the sea someday, and even in her fantasies Johnny Depp sports this completely deadpan expression, with a slight sneer that indicates that this is a guy who does not intend to enjoy himself ever again in his life.
I like Tim Burton's style, and the grim and hideous vision of London that he cooks up is very impressive. I can definitely tell that a lot of it is CGI, but the non-computerized sets fit in very well with the sweeping pans that are made over a city that doesn't really exist except in Burton's twisted animation.
And the blood... all I can say is that it reminded me strongly of the black knight in Monty Python. After a certain amount, it goes beyond yucky and just becomes silly. I think that's not a criticism, because Burton probably meant it that way.