I never saw Into the Woods
on the stage, so I have nothing to compare the movie to and I thought the movie was just dandy. But people who are familiar with the original version are grumbling about the cuts, and there's been criticism of Meryl Streep's performance as the Witch. Evidently in the stage production, there was some pathos in the Witch's role. As I understand it, the audience never sympathizes with the Witch but does come to understand her and perhaps feel pity. Streep's Witch is a cartoon witch (and a very good cartoon witch she is), but that's not how the role was originally conceived.
For me, the high point of the movie was "Agony" -- the duet sung by the two princes. Here we have two young men, brothers, basically in accord, singing of their two ladyloves -- but they still can't refrain from jockeying for position in their two-man hierarchy. Delicious.
A little cinematic synchronicity: two new movies about male British geniuses. The Theory of Everything
(Stephen Hawking) and The Imitation Game
(Alan Turing) feature stellar performances from the two leads, Eddie Redmayne and Benedict Cumberbatch, both of whom have been nominated for Golden Globes and will probably get Oscar nods in a couple of weeks as well. IMO, the Hawking movie is the better of the two, but only slightly.