Heh, I'd never noticed that one before. Disney did that quite a lot on their movies, actually. Even in movies as recent as Beauty and the Beast, where the dance at the end is step-for-step the same as the dance at the end od Sleeping Beauty (although that one may have been an inside joke) It's very common. Recycling animation cycles like that and pasting the specific characters on top saves a lot of time and energy, and when it takes thousands upon thousands of frames to make each scene, the animators are probably looking for any possible shortcuts.
Time and budget constraints could also be a problem; if they want to finish under budget and before a deadline, they're going to do anything they can to, well, econimize. If you watch The Jungle Book and The Sword in the Stone and pay attention to Wart/Arthur and Mowgli, you'll see a lot of similarities between the two. A few scenes in the movies are identical, just like that Robin Hood/Snow White comparison.
For example, in both movies there's a scene where the boy is jumped on by a pair of dogs, or in Mowgli's case, wolves, and they make the exact same motions and everything. There are all sorts of examples like that in loads of different movies, it's just a time-saving technique used by the animators.