This is complete and utter poppycock, both consoles are capable of outputting a 4k image although neither could render any modern game at that resolution.
Although the PS4 is a bit more powerful, the Xbox One can also render games at 1080p and there are many games on the XBO that do so. Examples of this are all 3 Forza games released so far, Halo Master Chief Collection and Gears of War Ultimate edition. Many other games use dynamic resolution scaling to maintain consistent frame rates. Unless you're pouring over single screenshots and technical articles I challenge anyone to be able to spot when this type of scaling is happening during active gameplay.
It's the very nature of console development that you have to manage the hardware resources appropriately to get the performance you want for your title. DirectX 12 will help improve things on XBO but will not be a magic bullet, rather we'll see a gradual slight improvement in performance over time, much like the life cycle of every console as devs manage to squeeze the best out of the hardware.
