It is really sad how it is 8 years later and this old blogpost analyzing a WebP pre-release version still holds:
https://web.archive.org/web/20120319...x/archives/541
I have done some recent tests and at the same filesize WebP was doing clearly worse than mozjpeg in a bit more than half of my test images.
libvpx and libaom do the same, they just blur anything to get good PSNR metrics, unusable for human perception