The Twitch.tv functionality on the PS4 and Xbox One are dramatically different.
On the Xbox One, you can watch ANY Twitch.tv stream. On the PS4, it is incredibly easy to stream to Twitch.tv, but you can only watch Twitch streams that are being broadcast through the PS4.
Xbox One Twitch.tv Breakdown
~Can watch any Twitch.tv stream
~No Sign In, No Chat
PS4 Twitch.tv Breakdown (1:40)
~Insanely easy to stream
~Can only watch PS4 streamers