If anything, this movie should really be called a sequel to Alice in Wonderland, although I don't know what the actual title of the movie should be in that case. The characters are all there, and some scenes (i.e. the tea party) are the same, but Alice is about 18 years old, this is her second visit to Wonderland (or Underland, as it's called in the movie, which is stupid and unnecessary), and the situations themselves are almost entirely new. In this version, Alice returns to Wonderland, and is supposed to slay the Jabberwocky, which will allow the White Queen to take over from the evil Red Queen. Of course, no one is sure she's the "right Alice."
But let's start with the queens. Yes, Helena Bonham Carter looks unnecessarily weird, but I think she actually did a fantastic job. Despite being a composite of the Queen of Hearts from Alice in Wonderland and the Red Queen from Through the Looking Glass, but hey, it's a sequel. A truly evil queen wouldn't have worked in this movie, so the humor and insanity that Carter puts into it made her into a much better character. Sure she was over-the-top, but that's kind of how she needed to be. The White Queen on the other hand: eh. I know Anne Hathaway can act, so I'm more inclined to blame the character than her, especially when it was a small part, but she had no personality, and her affectations came off as annoying, rather than a necessary part of her character.
Also, nerdy side note: Maybe this is mostly because I'm taking a class on Elizabeth I, but the Red Queen is absolutely Queen Mary and the White Queen is definitely (but less directly) Elizabeth. I mean, they even call the Red Queen the Bloody Queen! And the White Queen being somewhat trapped in her castle while her followers plan a rebellion she may or may not be involved in? Definitely the Wyatt Rebellion rewritten to be successful. I'm also 99% sure there was a picture of Henry VIII (Mary and Elizabeth's father) in the Red Queen's castle.
Anyway, if there's one thing that was too Burtonesque, it was Johnny Depp as the Mad Hatter. Of course I hate to say anything bad about Johnny Depp, but I think he had a little too much fun with this role. His part was much, much bigger than in the books, and to some extent the character development added depth to the plot, but it was mostly unnecessary, and I think it would have worked better if Depp toned it down a bit. You don't need to be a serious actor? Alright, we get it. You also don't need to change your accent every five minutes.
I have to say Tim Burton was right when he said he's never seen a version of Alice in Wonderland that captures the true essence (not that I've seen many versions, although I have a strong recollection of one with Whoopi Goldberg and some people on roller skates), but I'm not entirely sure he does either. He said he wanted to make a "warrior" version of Alice, which I don't think is the essence, but she was a lot more vulnerable than I thought. I think the movie succeeded because there was plenty of basic things (i.e. characters) for people who don't know the books well, and lots of little things for people who do know them well, but Burton also managed to create something entirely new. Framing the story with Alice having to kill the Jabberwocky may seem kind of silly, but I really liked it, and not just because that poem is one of two that I know by heart. It gave the movie purpose, and direction, and allowed Alice to really shine. Even the 3-D was done reasonably well, and wasn't nearly as gimmicky as I would expect from Tim Burton. All in all, it wasn't the best movie I've ever seen, but I liked it far more than I thought I would, and would definitely recommend it.