For this quick comparison study, we will take a few GIFs from http://iwdrm.tumblr.com/ and wikipedia, and convert them into APNG, WebP and lossy WebP using latest gif2apng 1.9 and gif2webp 0.4.3 tools with the following command line settings:
gif2apng -z2 -i500 Animation.gif
gif2webp -m 6 Animation.gif -o Animation.webp
gif2webp -lossy Animation.gif -o Animation_lossy.webp
Since first 3 animations in each test are identical (result of lossless conversion), the goal of the study is filesize comparison, not quality comparison. Lossy WebP animation (4th example in each test) is mostly provided to satisfy curiosity, not as a serious contender. Using GIF as the source is hardly ideal for lossy video-like compression, but gif2webp is currently the only easy-to-use tool to create such files.
In conclusion, APNG wins the filesize comparison over lossless animated WebP.
Conversion tools can be found here: