No two ways about it, large screens are better for many types of input.
Why mobile first is outdated
Intercom
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Screen size doesn’t predict “input” method (in my experience). TV’s might get better browsers, but most remotes are heinous for even basic navigation. Gaming consoles, like Xbox use various “devices” to input on your big screen (game controllers, connected phone app, hand & voice gestures).

So, my mind grapes jump to concluding that “device” matters as much as “context”… to say “device doesn’t really matter” feels like a risk to finding good design decisions.

Personally, I would struggle to know what UI is most appropriate without knowing the screen’s size, it’s location & proximity to users, the device that houses it and the device(s) that control it.

Enjoyed this article — good debate to be had here.

A List Apart has a good follow-up read from a couple years back (throw art direction into this mix, too). http://alistapart.com/article/surveying-the-big-screen