Maybe you create the menu you would like them to have, and not for the stomachfiller they do sell today 🤐
Then you could invite yourself ...
Good luck with your project.
How many pages is the menu?
I would go with Designer if it is just a 4 page design. Meaning one sheet of paper folded in half. Use two artboards one for the inside and one for the outside (the front and back) if it is more than four pages use an artboard per page then assemble them into the finished size in another document.
Since a menu is kind of a price list it must not contain text errors, respectively wrong numbers. Therefore APub can support you with features to give you most flexibility + efficient care and safety for your text. For instance Find & Replace, the already mentioned Master Pages, the concept of "Spreads" (facing pages for folded menus), the option to place Linked Resources (e.g. images) and finally "Sections" which can help when the variety of menus or layout variants increases within 1 document, which you additionally may mark with auto-text from "Fields" – these all are features which don't exist in AD and APh.
Also, of cause, you are free to combine the apps: e.g. for illustrations and photo editing, AD and APh will support you definitely more than APub. That means you could create all non-text in AD or APh and transfer those content as linked objects into APub, where you add the text. This way APub would do the main, "parent" document which contains the entire menu layout content whereas AD and APh would deliver parts of it.
However, this actually isn't a fundamentally necessary decision. You can start with AD and switch with any existing data if necessary. Of cause it would be quite useful to know the apps and their abilities and limits to do such a switch in the right moment. But I recommend not to use APh as the main, 'parent' app since it doesn't support you with various 'pages' (canvas, artboard) which will cause a cumbersome, confusing workflow for a bunch of menus with their increasing number of layout variants + updates.
Not existential here but nice to have: Different to AD and APh in APub you can switch the personas within APub, which gives you a quick access to major features of these apps without the need to leave APub.
For multiple page design, especially when text is involved, Publisher is the best pick.
You can create the basic layout of the restaurants menu as Master page(s), and fill them with content as you go.
Maybe these guys can compensate you, if not with money then with some of the best the kitchen can do 🤤
