In my opinion/experience, once you get past 24", if you only have 1920 horizontal (or smaller), the pixels are getting too big to add any benefit and just seem 'lo-res' ish.
I'm a software developer, and the PPI of the 27" or 30" 2560 x 1440/1600 monitors are about right for 100% / No scaling. A 27" 2560x1440 screen gives me 78% more desktop pixels than a 1920x1080 panel, which comes in super handy for all the windows and programs I'll have running when working. For 4K work, I use this V
iewSonic VX4380-4K 43" IPS 4K Monitor which actually replaced this
Dell P4317Q 43" monitor on my desk because despite it being 4K, the HDMI inputs were only HDMI 1.4 (Seriously?) and thus only 30hz. That size may seem huge, but the PPI is about the same as the 30" 2560x1600 mointors that were my mainstay for a decade, and is great for developer work.
Now, for hi-res video and photos, a 4K 24-27" monitor can be a better option, especially if the color calibration is excellent, like my 24" Dell P2415Q. Absolutely beautiful for images like that.
My wife has a curved widescreen
34" Dell UltraSharp U3415W on her desk, and it makes a great replacement for a traditional dual monitor setup. She frequently uses the Aero Snap feature in Windows to have to two full size document windows open side by side and it goes great with her workflow. The curvature may not seem like a lot at first glace, but it really makes a difference and makes using it more pleasant.
If gaming is your thing, you will want a really beefy videocard to game at 4K native res, and since this is the Mac Mini thread, that ain't happening, whereas a 2560x monitor will get you much better frame rates (like 2x+) vs a 4K, which is a good compromise.
As you can see, I'm not big on 1080p panels if I can have better, and that's partly because of the amount of vertical space. Every bloody website these days (and half the programs out there) seem designed for a mobile phone and/or embrace the *****y modern design principals of putting as little info as possible on screen with the least amount of visual contrast and distinguishing cues. Anyway, that means lots of vertical scrolling in a world where PC monitors are going more horizontal... *sigh*
Ok, that's my brain dump.