WebP should win over GIF. It's smaller, can be either lossy or lossless, supports full transparency, has animation, ... except for the fact that almost all GIF usage is (a) "clipart", (b) forums/comments/emails or (c) raw links (i.e. Imgur).
When I say clipart, I meant that most GIF image use would be people using GIFs made by other people. The Internet has a large treasure trove of GIFs that people will re-use from here to eternity. I doubt anyone will ever bother to convert the GIF to WebP.
Even if they did, if your browser doesn't natively support WebP[1] then you need a Javascript shim. Most people won't know what a shim is or won't be allowed to arbitrarily inject JS into the forum/comment/email. With raw image links, it's obviously not possibly to add a JS shim either.
I hate to say, but I think we're going to be stuck with GIF for a while longer...
And GIF's reprieve got extended thanks to Tumblr images of Tom Hiddleston mouthing words, of all things.
APNG's degraded support is possibly even worse for adoption. It has all the same issues as WebP (see the shim discussion above) bundled with the fact that people don't expect PNGs to move.
People either (a) don't know it's broken (i.e. think the single frame means it's a static image) or (b) know it's broken and chide you for using PNG instead of GIF.