I'd never read Just So Stories before, though I think I'd heard of one or two of them, and The Jungle Book is far more interesting a broader than Disney's version of it.
The Jungle Book has the adventures of Mowgli, but the Disney version only spans the first chapter and an episode in a subsequent one, but Mowgli's adventures in the book also relate how he killed Shere Khan (of course in Disney we just get the episode where he scares him off) and also how he tried to integrate into the village. In the book, Mowgli doesn't fit in with the wolves, or with the people.
But there's also this great story about Rikki Tikki Tavi, a mongoose that kills an entire cobra family, saving a little boy and his family from certain death. Don't you love the words "Rikki Tikki Tavi"? Great name for a lovable mongoose. So imagine my surprise when I watch a movie trailer while I'm still finishing the book in which Billy Bob Thornton tells a kid that it's okay to lie to his dad because he's from rikki tikki tavi or someplace like that! (Bad News Bears remake obviously). Spoiled the deliciousness of the name just a little. But not too much 'cause Kipling's got a real flair for storytelling and I loved Rikki Tikki Tavi (the name and the character).
Just So Stories is a series of "How the Leopard got his Spots" kind of stories, but the interesting part about these is the extent to which the narrator of the stories is engaged with the audience (a child, from the sounds of it). He repeatedly interrupts the narration to explain things, humorously, and in great detail to the child who the story is directed at. He also very humorously, and in great detail again, describes the drawings that accompany the stories, making comments about the limitations of working in B&W and the difficulties of representing things accurately. Very interesting from a narratological perspective.