I'm not going to tell you anything new here, but there are reasons to use GIF instead of video. WebM isn't supported on Safari & IE. H.264 isn't officially supported on Firefox (though I believe OS X and Window may now provide their own decoders that Firefox uses). To get a similar experience to GIF, you need two formats and it needs to be embedded in an HTML file using a <video> tag. Compare that to the GIF experience, where you link to the image and it works the same way everywhere.

There simply is not a video-based standard that implies "short, silent, autoplayed, looped video" in the way that animated GIFs do. There are ways to approximate the behavior in HTML, but none of them are perfect in the way GIFs are.