I prefer digital downloads and DRM free. CD/DVD take up too much space. Same with books. And I can have a NAS or a hdd to back up everything.

I used to like having physical copies, it feels like more of a thing than a virtual shelf on a website. But then I ran out of shelf space. I almost never do anything with those boxes and cases, so they're pretty much decorative. They've been on the shelf for a long time just gathering dust, I hardly pay notice to them myself anymore and I rarely have visitors who appreciate them. Thinking rationally, I should really get rid of them or at least pack them away.

Some of them are beloved classics that own me more than I own them and I could never imagine getting rid of them, but a lot of them I don't care quite that much about. Some years ago I thought I'd grab them from GOG sales and sell off the boxes. Did the former, but the boxes resist, they are still there.

As long as it's DRM-free, you can make your own discs. Multiple smaller games burned on DVDs and stored in cakes don't take that much space. I did this for starters when my GOG collection was small, but it's very cumbersome with updates and doesn't scale well to bigger games. Now I just download everything to a dedicated storage disk. I also have most of it on another disk that is stored offsite, but that's out of date and I'm not overly concerned about backups while GOG still exists.

always digital for me.

Do you want something that with a simple snap of a finger, you can have an extra copy, or a volatile media?

I prefer (DRM-free) digital. I see absolutely no benefits with retail CD/DVD versions, compared to e.g. GOG versions. Only drawbacks. I have maybe closer to 2000 DRM-free digital games (from GOG, DotEmu, HumbleBundle etc.) on a small 2.5" USB hard drive (2 terabytes); how much physical room would I need for so many games in a physical retail form? I'd probably need to move to a bigger apartment.

Plus, finding a certain game installer from that hard drive is definitely faster and easier than if I had a room full of 2000 retail games. Also browsing the games is far easier.

I think that is mainly because people tend to have more digital than retail games. Individual games are easier to remember when you have less of them (retail).

I still bought retail Mefal of Honor games twice accidentally, by buying both the Warchest and 10th Anniversary collections. The reason was that I remembered wrong that my 10th Anniversy bundle was a Call of Duty collection, not a Medal of Honor collection.

Also in the case of games which offer good DRM-free offline installers that are named sanely (e.g. GOG, DotEmu etc.), I can easily check from my hard drive where I keep the installers whether I have some game already, or not. If you choose to not to download all your games (but rather keep them on the store servers), then you'd need to log in to each store web page to check them.

If the CD stops working (scratched or something) what do you do?

You can burn your GOG game on DVD (how much is a blank DVD, 25 cents?) and print a DVD cover from here:
https://docs.google.com/spreadsheets/d/1L3z0_mVvsYw9cklgZuhP0-Xb7FFXhCQL-FcG8tGVssY/edit?hl=en_GB&pref=2&pli=1#gid=0 if you have a color print. If you don't, I'm sure you can print it somewhere else for a low fee.
If this DVD fails you can redownload the game and repeat the process. GOG wins.

Well, a physical disc can get damaged, or lost. Also, there may be drm on the disc, or the files wont work on newer operating. One of the points of Gog is that they update their product to run on most, if mot all newer os's. As for your concern of being tied to an online store, I quite agree, never trust anything with an internet component. What I have done for years is to have a hdd in the computer, aside from os disk. Then monthly add another hdd, copy over the data and pull it out and I to a plastic case. I then kept 2 onsite and 2 offsite. That way I always had a working hdd, 2 local backups and 2 offsite.

I have recently upgraded, I still have the onsite/offsite backup hdd's, once per quarter, but now I have a raid 5 device running 3*4tb hadds, so 12tb useable. That is then the main hdd with built in loss resistance and the others are desparate fallback position.

You probably wont wont to go so extreme straight away, buy 1 or 2 usb hdds and copy your downloaded files to these, they are then available as and when you want, and you can clean your system without these attached.

It's not a 'versus', it's complementary.
But, if you had to have only one, it depends on your usage as other said : many repetitive use is bad for physical medium, but reliability in the very distant future is better.

Fully agree.

I want to have the covers (or backs, at least) visible on my selves (showing off that "this is what I waste my money on"), yet the ease-of-use of not having to fetch the disc when I want to play it - same with music, movies, and books.

Games on GOG can be downloaded as much as you want. You can save the installer on your HDD or Optical Disc for later use. There are no restrictions when installing on other PC's and you don't need to log in to your GOG account to do so either. Once you have the installation files the game is yours, free from any online requirements.

I can play immediately upon purchasing a lot of the time, no waiting on shipping, won't get damaged, can make my own discs/covers. Yeah download is a hell of a lot better.

Why not both?

I'm well aware of that, but it doesn't feel the same having a cover and disc I printed by myself. On a similar note, I've printed only one cover and made a disc of only one game - and those are not even the same.

If that Tropico 4 is DRM-free on CD, go on with it. However if it's a Steam-copy in disguise, you're better off getting it here. CDs don't suffer from painful download times or slowing the internet for your whole household, and installation is just as easy and so is getting it home.