jpegoptim optimizes Huffman tables. Mozjpeg's cjpeg always does it, plus:
* jpegcrush/jpegrescan trick: tweaks details of progressive JPEG for maximum compression (each scan gets its own Huffman table, and JPEG can arbitrarily divide data into scans). That's 5%-10% improvement over jpegoptim.
* if you're creating a new JPEG or lowering quality of an existing one, then it uses trellis quantization. In the lossy compression step instead of naively throwing away data, it evaluates lots of combinations to find best bang-for-the-buck combination. That's an extra 5% improvement in quality/filesize ratio.
* jpegcrush/jpegrescan trick: tweaks details of progressive JPEG for maximum compression (each scan gets its own Huffman table, and JPEG can arbitrarily divide data into scans). That's 5%-10% improvement over jpegoptim.
* if you're creating a new JPEG or lowering quality of an existing one, then it uses trellis quantization. In the lossy compression step instead of naively throwing away data, it evaluates lots of combinations to find best bang-for-the-buck combination. That's an extra 5% improvement in quality/filesize ratio.