Yes and No, Sony doesn't make the effort to make it worthwhile in comparison. In some cases the difference between the two is equal. What i mean by this is that for both, the xb1 and ps4 games that ran an unlocked frame rate or struggled to maintain constant frames will run at full 60 frame rate or constant target the game originally was programmed for. Same for games that used variable resolution, those games will run full 4k at all times. They also benefit from quicker load times. So not too much of a difference really other than the games that struggled to run stable will run stable or better at all times.

So where do they differ? well xb1 BC games will have HDR apply to alot of BC games that didn't originally have them, such as KH3 and it looks wonderful on the series x. Xbox also uses smart delivery where alot of games that support it will upgrade to the series x version if available at no charge by default, most ps4 games do not do this and will run on ps4 configurations. XSX also has certain XB1 games that can run 60 or 120fps even if they weren't orginally programmed to do so (some might have to be enabled manually, you can look up a list of games that do this, it's called fps boost)

​

Another bonus for xbox is that a number of orginal xbox and 360 games work and some of them also are able to run full 4k and or 60fps and HDR, when Sony does not offer native BC from the 360-PS3 generation at all.

​

TLDR; Xbox does BC better and shows further commitment to game preservation than that of Playstation. Xbox may improve and add more features or games to the list while Sony has shown little to no interest in it.