That being said I have some trouble going back to my 1200p screens at work after being used to 4k at home. Surprisingly even for emacs and other work-related things 4K makes a pretty huge difference in my experience. Everything remains razor sharp even with a small font. I can split my screen and display a few full page datasheets and schematics alongside my code. No need to zoom in or anything. No aliasing, no pixels, I find it very relaxing.
I don't have very good screenshots available at the moment unfortunately but this should give you an idea of what's possible:
http://images.akamai.steamusercontent.com/ugc/10059888168078...
http://images.akamai.steamusercontent.com/ugc/10059888168007...
Here's Dark Souls III which looks pretty great at 4K but unfortunately doesn't manage to run at a solid 60FPS on my GTX 1080:
http://images.akamai.steamusercontent.com/ugc/84843325410407...
And here's an older game, The Witcher:
http://images.akamai.steamusercontent.com/ugc/84843969116367...
Those hold up pretty well at 4K. In contrast I present to you Wolfenstein: The New Order which often looks very mediocre and yet manages to run worse than DOOM:
http://images.akamai.steamusercontent.com/ugc/10059888168132...
Note the low polygon count on some of the models and the very low resolution of certain textures.
World of Warcraft: Everything looks the same, except text is prettier, item textures are more detailed, and spell icons suddenly have noticeable details. ("Hey that's a guy with a shield! I never noticed that!")
Dishonored, or other FPS-es: Far-away details suddenly are not lost in the haze of antialiasing. Wires and greebling on bridges are visible, and Look Good. HUDs and ammo displays seem to universally SUCK -- they are often not scaled in older games.
All the face textures in most older games end up supporting the higher detail textures, but it gets closer to the uncanny valley. (I notice this a lot in bioshock infinite.) I haven't re-played Wolfenstein.
It's much like looking at the same picture or webpage on a retina screen vs a non-retina screen. Text looks better, some other things look much the same. Anything vector-based (HUDs, etc) might look better.