So I (Carolyn) absolutely adore Into the Woods, and the movie adaptation is excellent. Here's some of my thoughts on the movie. First, what I enjoyed:
James Cordon as the Baker, Anna Kendrick as Cinderella, Emily Blunt as the baker's wife, Billy Magnussen as Rapunzel's Prince, and Chris Pine as Cinderella's Prince are all outstanding. Superb casting and performance. (Magnussen and Pine are particularly perfect and hilarious).
Daniel Huttlestone and Lilla Crawford (as Jack and Little Red Riding Hood, respectively) both gave good performances.
The music is just as excellent as the original. 'Agony', 'It Takes Two', 'On the Steps of the Palace', 'Your Fault', and 'No One is Alone' were particularly excellent.
The set and the costumes are all far better than the original.
*minor spoilers from this point onward*
I was glad that they didn't back down on the...er, metaphorical implications of the Little Red Riding Hood storyline (which I totally though Disney would cut out). They also didn't remove the more unsavory bits from the original: the blinding of Rapunzel's Prince and the Stepsisters, the, er, foot mutilation of the Stepsisters, the infidelity of both Cinderella's Prince and the Baker's Wife, the death of some characters, and the (relatively) unhappy endings for others.
Similarly, they didn't back down on the other great thematic ideas present in the original: the difference between good and nice and right, the idea of only falling in love with the concept of a person (destroying the idea of love at first sight), the idea that people can become enslaved to their desires, the idea that all of the characters' problems (at least initially) are all because of their parents (one generation screwing over the next).
(Also, THEY KEPT MY FAVORITE SCENE IN THE ENTIRE PLAY, aka the scene where Cinderella confronts her prince, which is so thematically important and poignant).
What wasn't my favorite (aka all the things that I think were better in the original):
Meryl Streep as the witch was interesting, but she didn't have the same...presence that Bernadette Peters did (although, really, no one does). I did think that her performance got better over the course of the film, though.
I was a bit sad that they cut out the character of the narrator, which also meant that there wasn't a connection between the Mystery Man (later revealed to be the Baker's father) and the narrator. Additionally, the separation of the casting for Cinderella's Prince/The Big Bad Wolf, as well as the separate casting for The Witch/Cinderella's mother was a bit disappointing (I liked the thematic implications created by tying those characters together).
The over-the-top hilarity and humorous tone of the original was lost, which led to some of the more tongue-in-cheek lines falling a little flat.
They did remove the reprise of 'Agony', which was a bit...disappointing, for fairly obvious reasons.
Rapunzel neither died nor went mad (as she did in the original), which did detract from the witch's character arc. In the original, Rapunzel doesn't simply reject the witch and cut her out of her life (as she does in the movie); instead, after her prince is blinded, she is banished to wander in the desert (where she gave birth to twins - also something that was cut). This leads her to go mad, which in turn leads to her being accidentally stepped on by the giant in front of the witch. Rapunzel's story is never fully resolved - she simply tells the witch to get out of her life and then she's not seen for the rest of the movie. The witch's death was also new, and I didn't mind that too much except for the fact that it meant that she wasn't actually present when she sings 'Children Will Listen' (an incredibly thematically impacting song, the sort of end message that is left for the audience); instead, it is relegated to a softer background song and the focus is on the baker as he talks to his son (in the original, the baker is talking to his son at the beginning of the song but the focus is mostly on the witch as she sings). Thus the change from "children won't listen" to "children WILL listen", which communicates the key thematic idea that while children may not obey their parents, they will absorb their parents' words and the twisted messages sent with, is almost lost.
Watch the Official Movie Trailer: