Unless you work for Microsoft's PR department, it's generally accepted that PS4 is more powerful than Xbox One. But, it also draws a lot more power.
An analysis by AnandTech shows that PS4 draws more power than Xbox One while playing a game and while sitting idle. In terms of Blu-ray playback, Microsoft's box is far more efficient (somewhat ironic, one could say).
However, standby power consumption is comparatively high on Xbox One. The reason for this is likely Kinect. In standby mode, you'll be able to turn on Xbox One with a voice command: "Xbox, On."

It's true some times in not even plausible
Both my PC and my 360 are hardlined to my router.
Absolutely, but cords aren't always practical.