Why the size difference is so large
GIF stores each frame more or less independently, subject to a 256-colour palette. There is some optimisation — storing only the changed rectangle between frames — but nothing resembling motion prediction.
Animated WebP applies the same techniques its still images use: each frame is predicted from what came before, and only the difference is stored. Since consecutive frames of an animation are usually very similar, those differences are small.
The result is commonly a file three to ten times smaller, in full colour rather than 256. It is not a marginal improvement.