I found Into the Woods interesting because it seemed to stay in line with the fairy tale tradition more so than Willingham's Fables. Both seem to have a sort of modern day twist with Fables in particular placing fairy tale characters in the modern world. Into the Woods was relatively true to the originals, but there was always a hint of "We know this is silly and wouldn't really happen in real life" to them. The actors were great at making jokes about their characters without making it seem as if they were in fact mocking them.
I think it is quite clear that both Into the Woods and Fables are more recent pieces because neither takes fairy tales as they were originally intended to be interpreted. Fables places fairy tale characters into a more dramatic world. Fairy tales typically aren't dramatic, at least not to the level of a comic book so seeing the characters in such a dramatic way is intriguing. Into the Woods is truer to the originals than Fables. It is lighthearted and is more aligned with the way that we think of fairy tales today. It's silly and fun while also teaching a lesson.