WebP is designed to be better than JPEG but whether it will succeed has yet to be seen. Looking at comparisons
here it seems WebP looks smoother but also looks a lot less detailed, like blur has been applied to a JPEG of the same size.
You don't often get something for free and in this case the only way you could do that is if you've managed to improve on our current ideas in
Coding theory. This means that everything else you do will cost you either in file size, picture quality or processing time.
First a bad example

(original PNG) -18,084 bytes (96 quality JPEG) - 10,851 bytes (95 quality JPEG) - 9,884 bytes
Photos work better

(original PNG) - 267,524 byte (95 quality JPEG) - 59,033 bytes
Also note that the JPEG method is alive and kicking in the very latest
video formats (along with the closely related interframe compression).