Will the pixel density difference be visible between 4K and 2K monitors at 27" size?

IMO "sort of". Its definitely better and sharper, but native 4k content is pretty rare.

I'm looking at a 1080p and a 2180p display right now. I do do some sort of upsampling in my video player for 720p video and it looks fine. (Would screenshots be of help here? I dunno).

There's a lot of disagreement over whether 4K is worth it. Wirecutter doesn't explicitly suggest 4K displays 'cause they feel there's little benefit.

That said, I've worked in the vfx industry and no one worked in 4K. I can't remember what our 'standard' displays were but they're pretty crap. We used fairly standard Dells, typically older ones that were lying around. Good monitors would be 1080p or 1440p color calibrated. There's more concern over color calibration, and general real estate, and most work's done on 2K anyway. I'm not going to suggest exact models since I don't know whether my NDA at my last job covers that or not. Least as of this year, it doesn't feel like it's an essential tool for a professional visual effects or video rendering artist.

Depending on the sort of work you're doing, it's going to range from 'it doesn't matter' (you don't need 4k for modelling, or even texturing) to 'Just get a TV to see what it looks like' (if you want to see how 4k looks like, and most TVs have lower pixel density at 4K, since they are bigger) to "OH MY GOD IT IS AWESOME" (If you're a coder, or want a good general purpose high resolution display).

That said, most native 4K content is gloriously lush in many cases, but that might be cause they're made using really good cameras, and meant to showcase 4K. I've not managed to get my paws on a movie or TV show that's native 4k. I'm eagerly looking forward to netflix coming here for science.

The next question is "can I tell the difference?"

It depends on your distance from the screen. rtings has a great interactive site for working out these things. That said, they have a handy visual chart

And well, if you're sitting between... I'm estimating one and a quarter meters, and 2 and a quarter meters, UHD may make sense at 24 inches.

Puget systems actually does the math, and considers things like visual acuity if you like more science. TLDR/THDM (Too hard didn't math) - Yes . They also have a lovely spreadsheet on google docs if you don't want to do the math

Now, there's a few other factors to consider.

My 27 inch UHD screen beats the pants off the 24 inch 1080p screen I have in every respect.Pixel density (which on a 27" UHD display is 163 ppi) is essentially good enough that you can't 'see' the pixels. Compared to a 24 inch (admittedly inferior, TN) screen side by side, the pixels on a 24 inch are visible compared to the 27 incher, with the 27 inch display at 1.25x ui scaling, and the 24 inch at 100%/native.

Its even better in terms of pixel density than the legendary T220p, which essentially was designed to have a resolution like print media

However that's not the only reason its better, and not the only thing to look at. My screen is IPS, which is a significantly better technology. Its colour calibrated at the factory.

If it's in your budget, and you're willing to spend the extra scratch for a machine that can do what you want in 4K, it's definitely worth it. That said, when you can get a reasonably good setup for a few thousand less, it depends. I don't think unless you are working at 4K, its really going to be something that would help rendering though. Were I designing a setup for a 3d artist, (and building around a fairly powerful workstation), I might pair this up with a good (or mediocre) 2k display and get the best of both worlds, since you can review work at both resolutions

We're also at the point where 4K isn't common enough to chop too many features on mainstream monitors, the useful features (SST, mainstream outputs) are common on current displays and with some decent comparison shopping, you could probably buy one with a great feature set for not too much money. Jeff Atwood has three, and the excellent p2714q that I have is a hair under 500USD.

That said. The real question is "should I buy one?"

My usual answer would be not yet. The content isn't there, video cards struggle with rendering 4K video (I have a 980ti, and it tends to redline with most games, and the FPS tends to be decent, not spectacular at 4K). In your case though, it may make sense, especially if you intend to work with 4K, or code a fair bit. The extra real-estate, and sharpness is awesome enough that I'm looking at a second 4K display when I can afford it.

Let me start with a caveat. The answer is very dependent on the nature of the content. Your eyes can detect miniscule high-contrast objects, like a bright speck of light on a black field or a black speck on a white field. Resolving differences between adjacent colors is different. If you are looking at laser printed output, for example, a 200 dpi black on white fax will look crude; you need 400 to 600 dpi for text characters to look smooth. On the other hand, a 200 dpi 24 bit photo will look pretty good. With a moving image, you're dealing with visual persistence, which has even different characteristics. So this kind of question is difficult to answer precisely.

That said, we can do some math. A 2K (assuming 1920 pixels), 27" screen will have a pixel density of about 82 ppi, and a 4K will be about 163 ppi. With normal eyesight, If you get within a few inches of the 2K screen, you will be able to easily see the individual pixels. You could probably notice them at a normal viewing distance with a still image, or if the pixels are high contrast.

With a 4K screen, high contrast pixels would be discernable from a short distance, but something like a still photo would probably require magnification to see the individual pixels clearly. From a normal viewing distance, you could detect high-contrast pixels, but would have a hard time making out individual pixels in a still image.

With video, individual pixels aren't visible if they aren't high contrast (essentially persistent noise). However, if you were to view, side-by-side at normal viewing distance, a video at the full native image resolution that each screen is capable of displaying, you would probably see a sharper, more subtly-detailed image (more "photographic"), on the 4K screen.