When they were growing up I allowed them to be bombarded with information - TV on, web access, phones from an early age - and they've developed the ability to filter it quite well and just ignore things that don't interest them.
The only down side is:
"awww dad I didn't get anything done today" "why, son?" "some Internet happened"
Try watching a slow movie like Gattaca at home, with a dozen devices and apps competing to take your attention away, and see how many people drift off and watch it from the corner of an eye or don't even finish it at all. Does the movie deserve that? Maybe; if only short-form content or frenetic Avengers-like action can hold people's attention from start to finish, then that's how it is. But I, for one, appreciate immensely when people commit fully to something, the way it was intended to, for better or for worse.
And that's why I love the movie theater.
That said, and for all the love I have for computers and even for my Nexus tablet, I fear I'll become an anti-smartphones curmudgeon soon. I already feel uncomfortable when everyone takes theirs out right after lunch, killing any possibility of a conversation.