Not sure on Witcher, but the benefits are simple. The easier a game is to get up and running, the more time you have to optimize it and enhance it. As an end user, you benefit by receiving a product that has been improved by virtue of the extra time they gain in development. Now this benefit will vary from title to title, from engine to engine, depending on the needs of any specific product.
If the only benefit you want is an earlier release date, then yes from that perspective you are not gaining anything
The end result isn't the same though. If the PS4 was more difficult to develop for and took longer, you'd get less optimization and less improvements. There is always a finite time to develop anything, so obviously programmers love when they find ways to gain more time.
Ghosts wasn't a mess on both consoles, but there was a problem with the PS4 version initially because it actually ran way faster than 60fps, causing uncomfortable judder. From what I understand that was fixed in a patch some time ago, but I haven't been able to test that for myself.
On Xbox One, the game was 720p and had numerous other little effects looking better on the PS4, but it did not have that initial multiplayer framerate glitch, so it seemed to run better at first there. That was where the dispute was coming from, since people did not know the cause of the PS4 judder at first.
It is shown on your screen. It's only a matter then of how perceptive a user is. For example, the Tomb Raider on PS4 has a better framerate, better depth of field, better textures at times, better AA, better everything, essentially. Even certain cutscenes on XBO were 900p. That's a ton of real world differences.
Obviously however you will always see the biggest differences in games designed exclusively for the console. Look at the insanity behind the visuals of The Order's cathedral scene for example or the way Driveclub looks. Similarly on XBO's end, look at how Quantum Break looks and Sunset Overdrive. Very impressive looking titles, designed from the ground up to take advantage of the systems unique architecture.