Google WebP vs Mozilla mozjpeg vs. Microsoft JPEG XR

Google is pushing and supporting WebP.

Mozilla is pushing and supporting mozjpeg.

Microsoft is pushing and supporting JPEG XR.

Everyone trumpets their favorite format's superiority. The size of a compressed file can be measured, but the quality of lossy images is subject to human interpretation. How do we compare our choices?

Are these formats and their codecs going to live side-by-side and be supported by most major software, including Apple's, or is the battle going to be bloody, with only some format(s) emerging victorious?

PNGs were invented to avoid the Unisys patent claim on the GIF compression format, but once the patents expired the GIF format became free for anyone to use. Even though it was designed for a world of dial-up modems, it's ability to do animation seems to have given it everlasting popularity.