In lossy compression quality setting affects file size much more than choice of image format (e.g. there's 15-30% difference in best quality/filesize between old codecs like JPEG/J2K/VP8/JXR, but within each codec's settings range the file size can vary by 300%), so having a codec that picks the lowest good-enough quality is very useful.
Compared to MozJPEG:
- it's tuned for higher-quality images (butteraugli is said to be best for q=90+, MozJPEG's sweet spot is around q=75)
- it's much slower to compress (both produce standard JPEGs, so decoding is fast as usual)
- MozJPEG doesn't automagically pick quality setting, but you can find optimal quality using an external tool, e.g. https://github.com/danielgtaylor/jpeg-archive