First of, on Android, the camera doesn't magically scan the QR code. You have to download a separate QR code scanner app for that. My wife and my parents all have Android phones and have no idea what to do when they see a QR code like that. The waiter usually just says "point your camera to it" because apparently everyone in the world assumes you have an iPhone and that's how it works there. When it doesn't work the waiter now has to do tech support on a random person's phone.
Second, as others have said, the social aspect of looking at it together is totally lost. Which is quite big IMHO.
Third, scrolling through a PDF or a page on a tiny screen makes it much harder to grasp the entire menu quickly. On a paper menu, I often just jump around and get inspired by the various dishes. Randomly scrolling up/down/left/right on a tiny screen feel awful compared to just letting your eyes drift.
My vote is for a QR code and paper menus. Let the people decide what they like without excluding elderly or non-tech savvy people.