AFAIK JPEGmini has much better psychovisual optimization than libjpeg, so I think their claim that they can compress JPEG better within limits of the format is fair.
The way you encode lossy formats makes a lot of difference. For example the same x264 encoder gives dramatically worse results when aiming for optimal PSNR rather than using its psychovisual optimizer:
Is it not a bit ironic to be linking to x264 developers to support the thesis that a new H.264 encoder can be twice as effective in compressing H.264 than the competition?
Either they've done something magical and can outcompress x264 to that degree (i.e. in the ballpark of HEVC, yet without breaking compatability), or they're comparing against a terrible H.264 encoder and they've just wrapped x264 in a proprietary shell of BS (and/or they're liars?).
