I might be a bit late to replying on this one.
I am a big believer in promoting web apps over native apps, here at Poniverse we have written all of our sites (minus the forums) using AngularJS (This is a js framework that can be used to help to create html webapps).
However in my opinion media websites in the smartphone world are extremely subpar in their ux and even for desktops (moreso music sites than video sites because I want to use my media keys). You do not get access to many functionalities that a normal media app on the phone world, notifications, media controls (the play/pause button on some headsets), access to offline storage and plenty more that a native app would provide.
So I say, that those types of Websites, provided you trust them, do deserve to be used with a native app