This is sort of a tough review to write because, if you saw The Nightmare Before Christmas and loved it, you're going to see The Corpse Bride. If you didn't like it or didn't see it, chances are you're not going to know or care what the fuss is about.
I'm kind of in the intermediate position of not having really liked Nightmare when it came out, but now I appreciate it a lot more. At the same time, I've only seen snippets of it recently and haven't watched the whole thing in years. In any case, I would say that The Corpse Bride feels like a somewhat rushed, slightly half-assed attempt at recapturing Nightmare's feel.
With the caveat that I haven't seen Nightmare in a while, I believe Corpse Bride to be far more technically proficient. The models and animation are amazing, the scenery is well done and cohesive. There's an interesting color scheme where the overworld is all in greys and blacks, while the underworld is very colorful. There are some notably fun character designs, particularly Mr. and Mrs. Van Dort and Mr. and Mrs. Everglot. And, I should say, the movie is quite engaging as you're watching it. It's not in any sense a bad movie.
Still... I would say it has two major problems. The first is that what's there is good, but there just isn't much there. For one, it's very short, an hour and fifteen minutes. You're sort of going through and see hints of interesting plots coming, but they never really develop. There's a constant sense of "This is building to something cool!" and it maintains that sense of impending greatness until it just suddenly climaxes and ends. And the length isn't the only problem in this regard. There are some songs, but not very many (four, if I recall correctly) and none of them are very catchy. You feel like there might be a great song around the corner, but then the movie ends and the great song never materialized. There are some interesting characters, but the movie's too short to develop them and there's not nearly the ensemble cast there was in Nightmare.
The other problem is that it feels like a rehash, which is probably related to the shortness of the whole thing. There aren't a lot of original ideas in it, and it's strictly by the numbers (though, granted, by the numbers as laid out in Nightmare, which makes it original enough to stand out). In general, it just seems like it was made to cash in on the cult popularity of Nightmare, making it feel like yet another in the endlessly-expanding genre of "Sequels that had no compelling reason to be made."
All of this makes it sound worse than it is. It is, as I mentioned, engaging and fun, but it's not a movie I'm anxious to see again. There are some genuinely great scenes, such as the scene of Victor and Emily playing the piano, or the scene where the dead rise for the wedding party. Still, it's being pitched as the next Nightmare Before Christmas, and if you go in expecting that, you're likely to be disappointed. I'd recommend it, but see it at a matinee or discount price if you can.
As a side note, according to the end credits the Pilgrim's Chorus from Tannhäuser was supposedly played at some point. It's one of my favorite pieces of music, but I didn't catch it. I may have to watch it again to search for it, at some point.
UPDATE: And now that I've posted my thoughts and started looking at the professional criticism out there (to which I was blind prior to posting my review) I feel vindicated in my luke-warm reception by the fact that Stephanie Zacharek of Salon, the Wrongest Critic in the Business, absolutely loved it. She does make one salient point that I probably ought to have mentioned: it's great that they did this movie using stop-motion claymation, without a bit of CG. Bravo on that count, and kudos for the reference to Ray Harryhausen near the beginning.
