PDFs do nothing to improve SEO. They cannot be indexed by search engines, such as Google. Additionally, if you feature your menu on services like Google My Business, you'll be performing these updates twice.
Editing a PDF requires a word processor or graphic design software. They must then be exported and re-uploaded to your site every time a change is required.
In other words, PDFs do not display well on smaller devices such as phones. Your customers have to pinch and zoom to read small text on small screens.
For customers that don't speak the printed language, you have few options. Your customers can use Google translate's phone app and run your finger over the PDF picture, or you can make multiple PDF menus in each language.