Keep in mind WebP is essentially a VP8 I-frame in a RIFF container [1]. VP8 is the predecessor video codec to VP9; VP9 being the codec targeted by its makers to be in competition with HEVC which is commonly deployed inside HEIF -- whether they succeeded in this promise is an exercise left to the reader, possibly by following sources such as the ones compiled on Wikipedia [2].

But not all compression techniques that are applicable to video are relevant with still images. WebP's performance has been evaluated and some have found it lacking [3], while some have found it good [4].

Discounting the fact that the HEIF container has some useful features on its own, the picture inside is often an HEVC I-frame, which is the same idea as Fabrice Bellard's BPG. Therefore, comparisons between VP8 and BPG may also be indicative of typical HEIF-as-it-will-be-typically-deployed performance.

[1] https://developers.google.com/speed/webp/docs/riff_container [2] https://en.wikipedia.org/wiki/VP9 [3] https://en.wikipedia.org/wiki/WebP#Criticism [4] https://blog.cloudflare.com/a-very-webp-new-year-from-cloudf... [5] https://bellard.org/bpg/

Personally I'm not impressed with the quality of the lossy encoding, it's not enough of a improvement on JPEG to make it worthwhile, for lossless however it's the best format I know of right now, compresses MUCH better than PNG, and both compression and decompression is MUCH faster.

FLIF compresses better than webp, but it also compresses/decompresses more slowly, and the difference in size is quite small so overall for lossless compression, WebP is my choice.