In the case of a PS4/PS4 Slim....
The Input on the XBO S doesn't need to add 4K, since the image is not 4K and since the output stage is what upscales the image.
HDR is HDR, if Ps4 can pass HDR over hdmi 1.4, then the input on the XBO S is HDMI 1.4, so you get 4K upscale + HDR as the output on a title that supports HDR.
Lag? In this case usage: The input lag is preferable thru the console outputting a 4K format than BOTH the input lag + display lag of letting the HDTV process the image real-time . LCD's already have lag simply displaying a native signal, upscaling adds several frames of lag on its own compounding it.
Upscaling is always preferable before it hits the display. you want the display to simply display a native image.
PC I i7 3770K @4.5Ghz I 16GB 2400Mhz I GTX 980Ti FTW
Consoles I PS4 Pro I Xbox One S 2TB I Wii U I Xbox 360 S
