We set default quality parameters for PageSpeed with the goal of producing equal quality images between WebP and JPEG, on average (quality 80 for WebP, 85 for JPEG), but you're right that in this case the WebP image is more distorted as measured by SSIM. Sorry, and thanks for catching this!
Testing now with this image, to bring the DSSIM-measured distortion on the JPEG up to 0.015 [1] I need to encode it at quality=69, which gets me a file size of 24317 [2] bytes to the 20158 [3] I had for the WebP. This is 17.1% improvement for WebP over JPEG, as opposed to the 47.7% improvement I found before. This is all with libjpeg-turbo as included by PageSpeed 1.9.
Running mozjpeg (jpegtran) with no arguments built at commit f46c787 on this image, I get 23870 bytes with no change to the SSIM [4]. This is a 15.6% webp-over-jpeg improvement.
It looks like:
1) We should run some timing tests on the mozjpeg encoder, and if it's in the same range as the WebP encoder or not too much worse switch PageSpeed from libjpeg-turbo to mozjpeg.
2) We should check that quality-80 with WebP is correct for getting similar levels of distortion as quality-85 with JPEG. Is this image just a poor case for WebP or is it typical and something's wrong with our defaults?
[1] Technically, 0.014956 with JPEG compared to 0.015060 for the WebP.
[2] http://www.jefftk.com/kitten-demo--ssim15--pagespeed.jpg?Pag...
[3] http://www.jefftk.com/kitten-demo--ssim15--pagespeed.webp?Pa...
[4] http://www.jefftk.com/kitten-demo--ssim15--mozjpeg.jpg?PageS...