mehmet.dogu.ozel :
Thanks man, I really appreciate your detailed explanation... One more question though, instead of paying more on the ps4 pro or Xbox One X, I can solve the problem by buying a monitor which has a decent response time and refresh rate and play the ps through the monitor, right?
Unfortunately, the PS4 like all computing devices, really is a product of its time, though much improved over the PS3, the limitations of the PS4 are really brought home when you use it on large format high resolution displays. In my case I have a PS4 sitting upstairs in my media room hooked up to a Sony 1080p tv. Which is a perfect partnership for the PS4.
Unfortunately there is not much a display can really do to make up for the shortcomings of the device attached to it. Sure it can upscale, sharpen and alias but those techniques have their limits. Displays and the devices they connect to go hand-in-hand, If you connect a high performing PC with a great GPU like a 1080Ti or 2080Ti to a low refresh rate 1080p display, you'll be limiting its capability because those cards are capable of so much more.
However, the PS4 is at its limits generating a full 1080p frame, and it cant manage that when things are really busy (like a high action sequence). Given that the display limitation of the PS4 is 1080p its best to pair it with that kind of display. It's just not possible for modern displays to extrapolate the 4 fold increase in image detail required to drive a 4K panel from a 1080p signal. In fact even some older PC's have problems with this if they do not support the later versions of HDMI and the HDCP protocols. Running games at 4K 60 FPS requires a huge amount of visual data to be exchanged with the display (typically around 1-2Gbyte/min) and that speed isn't possible on the earlier standard. The PS4 just doesn't have the hardware support to do this. Connecting a PS4 to a 4K display would be like driving a Maclaren 570S in rush hour, sure you can try it but you wont get anywhere fast.
However the PS4 Pro is pretty great, its compatible with your older library, and if you pair it with a 4k screen you are seated a couple of meters away from you'll not notice the upscaling that much, and in some titles it runs native 4K. Just bear in mind that the PS4 Pro does not support 4K blu-ray playback if you decide to grab one.
Remember, the best results always come from properly matching your devices to their capabilities.