Adobe tries to overcome some of the shortcomings of PDF compared to HTML+CSS (both may contain JS) while maintaining its two main advantages: same static design wherever possible in a single file. Both can also be considered disadvantages sometimes.
From a website user perspective, a HTML+CSS(+JS) menu has several advantages. Some of them could be done in PDF, too, but most generators don’t support them (easily). An online menu is integrated into the site, i.e. the user doesn’t have to switch from browser to document viewer app and with seamless design the menu feels just like any other part of the site, hence will have a navigation entry and semi-automatically adapt to the viewport size.
An online menu can also be interactive, i.e. users may sort (e.g. by price, meat, course, size), filter (e.g. for vegetarian, alcohol/dairy/gluten, special offer, children menu) and search the entries.
Visitors can also use assistive technology like screenreaders, magnifiers, translators and currency converters.
Paper and PDF are bad at providing videos or dynamically enlarged pictures.
If the website menu already contains an order form, it may be easily possible to code a tablet app in the future which would replace paper menus.
The data can also be reused for electronic billboards – many fast food places now have large TV screens atop the counter listing menu options and prices, which enables quick, simple, unnoticable and even frequent entry and price changes (e.g. lunch-time specials and seasonal offerings).
If the print menu and the website are generated from a single source, which might also connect to whatever program the restaurant manager uses for accounting, then there’s hardly any reason to put the PDF on the web, at least neither as only nor as default option. This assumes the same persons edit the backend of website and print menu.
In conclusion and from a UX perspective (on both, frontend and backend), restaurant menus should be normal database-driven webpages.
PS: I have seen guests in restaurants use their phones to look at the online menu instead of the printed one lying on their table, just because of the mentioned benefits, and in South-East Asia waiters have handed me a tablet pointed to the restaurant’s website, because the print menus were only available in the local script and without pictures.