Quoted as incorrect and to make such claims is misleading.
As an example...
To quote Eurogamer, regarding PS4 and X1, Arkham Knight: "From top to bottom, these two versions are otherwise identical. The resolution difference is the only aspect that divides the two visually, and both deliver results eerily close to Epic's 2011 demo."
Additionally it is well known that the X1 has far better media functionality and compatibility than the PS4. Does it have Kinect, nope. Does it have hdmi passthrough, nope. Does it have windows 10 streaming, nope. Hell you can't even play many mkv files on the PS4.