Based on separate statements from both Sony and Microsoft, it has been confirmed that you will be able to connect the PlayStation 4 to the Xbox One’s HDMI port and stream the PS4 through the Xbox One. Microsoft executive Albert Panello confirmed that PS4 games could run within an Xbox One overlay.
Panello also confirmed that, using this setup, players can multi-task between the two rival consoles. “Any application can be snapped to a game… so if you wanted to be playing Ryse (an Xbox exclusive) and Killzone (a PlayStation exclusive) at the same time, you could snap that,” he said.
Shuhei Yoshida confirmed on Twitter that they had decided to reverse policies so that the PlayStation 4 will not block any external device taking its HDMI feed to stream or record it. Evidently, any console that outputs to HDMI can be connected to Xbox One in the same manner. Such consoles include Xbox 360, PlayStation 3 and Wii U.
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Not many people will do this (not to mention that not many people will own both consoles), but it is nice for consumers to have the options. This allows them to create an all in one media hub without having to change inputs or connections.