Since Xbox Released the remote play for the Xbox One people have been questioning if Sony would do the same. There is already a way to play remotely via the PS Vita, and someone has made a 3rd party PC remote play app called Remote Play PC, but there is no official way on the PC to stream the PS4, at least not yet.
Shuhei Yoshida has announced, via twitter that Sony is actively working on a PC remote play application, for the PC and Mac.
Some people asked if we plan to provide Remote Play function to PC, and yes, we are indeed working on an official application for PC/Mac. 😀
— Shuhei Yoshida (@yosp) November 27, 2015
Few details were revealed beyond the fact they are working on it, but with the ability to use the DualShock 4 on the PC already, and the remote play proving itself with the PS Vita, it is not hard to imagine it will work just fine with the power of the PC.
As these consoles start to match feature for feature, just before the holidays, it is anyone's guess who will be the dominant choice for gifts this year. What ever anyone chooses, with features constantly being added to both consoles, there is no way they will be disappointed.