Prince is an elegant and advanced PDF rendering engine, used by commercial publishers such as Hachette. All Pressbooks PDF themes are built to style Prince PDF exports.
mPDF is a less-powerful utility that we don't actively support, and no Pressbooks themes have been built to style mPDF outputs.
Using Prince, you will get professional-looking, typeset PDFs, designed per the theme, ready to go to a Print on Demand service, or offset printer.
Using mPDF you will get (as far as I know) a basic PDF output that is readable, but not styled as a printable book, and without any change from one PB template to the next.