Kodi, as you may recall from a decade ago, has its roots in the old Xbox Media Center. It grew beyond that OG Xbox a long time ago and runs on just about anything these days, although things like Raspberry Pi 4s are a common (and performant) choice for dedicated hardware. It is open source. Kodi is primarily a media player (load files from local or regular-ass SMB NAS, and play them), and it is very good at doing that correctly (correct screen resolution and refresh rate, correct audio format selection and output -- that sort of thing). It generally operates in a largely standalone configuration.
Plex also has its roots in XBMC, but it went in a different direction: It is split into two parts: The Plex client, and the Plex server. It's a very different beast: While Kodi can play whatever you throw at it on your own LAN, Plex can let someone three continents away play that same thing over your WAN -- with official Plex client apps from the usual official app stores [from Apple or Google or Roku or whoever], so it's very approachable. But the server can be heavy (it does video transcoding), and that server also has features that want to be paid for, and it is not exactly cheap.
Jellyfin, meanwhile, is a fork of Emby. Both Jellyfin and Emby exist because Plex is neither free nor open. They do many of the same things that Plex does, and also have a client and a server component.
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I use Kodi in my living room because it is the thing that works most-correctly with my particular home theater gear.
At my parents' place, they use Plex, because it is easy for them to use (the interface is easy, and I maintain the Plex server) and they aren't as picky as I am: They're happy if there are moving pictures on the screen and sound coming out of speakers. (I have the bandwidth to support remote Plex usage, because it does transcoding, but I do not have enough bandwidth for them to run Kodi with my video library.)
I don't use Jellyfin (or Emby) because by the time I learned of either those, I'd already paid for Plex.
It is absolutely ideal if what one wants to have is a dedicated media player appliance and -- like any other cromulent video playing appliance -- it Just Works.
But there's a ton of other ways to get Kodi running on Raspberry Pi hardware.
For instance: There was a time when I was running Kodi under RetroPie, so I could combine antique console emulation and video playing on one [at the time] Pi 3.
little correction: Jellyfin exists because neither Plex nor Emby are free or open.
I believe some use Kodi as a direct play frontend for a media server. But the native apps are pretty good these days and can direct play ~everything.
The other strong point is the plugin ecosystem. In particular, the Debrid plugin which allows you to consume content without needing to invest in storage. Stremio is an alternative to Kodi in this area afaik. Various IPTV streaming plugins also exist.
Results have been pretty good, although it suffers from some non-intuitive UI design... the sort of which also plagues other media applications I've tried.
Let me try it on my computer... OK, specifically, Kodi says, "your library is currently empty. To populate it... enter "Files" section, add a media source, and configure it."
So I did that, and navigated to a directory that contains some video files. There's no way to "add" it. Clicking on it opens it. And so on for contents. If you click on a video file, it just plays it.
Then there's no control for going back to the home screen. You can go up to a parent directory, but once at the top you're stuck there. On an Android TV you have a Back button on your remote, but there's no control for it on the computer UI.
This is disappointing.
I think right mouse click is "back" by default. Everything is configurable to a huge extent as well if you don't like the defaults.
Tab and backspace are useful x to stop playback
I use Kodi for this purpose - direct view on a local device - and Jellyfin for 'remote' applications, e.g. for making our extensive photo and video collection available to family members. Jellyfin is a media server while Kodi is an extensible media player which happens to have some limited support for remote access/streaming. In other words they are complementary, not in competition. I have never used Plex nor felt the desire to do so.
It has been calibrated for the colors to be as correct as possible. It's from a time before smart TVs. (Heck, it's from a time before LED-backlit TVs -- it's got fluorescent tubes in it.) But it has HDMI-CEC, and it cheerfully outputs both DTS and Dolby Digital on its optical TOSLINK port so as to connect to [cheap!!!, and sometimes even awesome] surround receivers of similar vintage.
If you find a Samsung of that age that hasn't been smashed, it probably won't work reliably as-is: They used bad capacitors in the power supply -- bad enough that they lost a class action lawsuit about that at least once.
(But good caps are cheap, and they're ridiculously easy to swap out on those single-layer PCBs. The only trick is to spend the extra few dollars and replace every single capacitor on the power supply board, and not just the ones that seem to be bad: All of the factory caps will turn bad eventually, which is something I learned the second [and hopefully final] time I took it apart to fix it.)
Both have great pictures, no dead pixels. The biggest issue with thrifted TV's is that they don't come with stands so you need to get a wall mount or contrive a stand of some sort.
I would heavily recommend against anything Samsung. There always seems to be something wrong with any Samsung being sold 2nd hand.
With Kodi, the primary consumption is at the place where Kodi runs and typically there is no server. kodi can support lots of plugins and act as a interface for different media sources/apps. This makes kodi feel a bit clunky.
With Jellyfin & plex the primary place of consumption is a client running on your favourite device while the heavy lifting of downloading and transcoding is done on the server. This abstracts the different media sources from the clients and clients are just focused on consuming media.
Family used plex cause that’s the easiest, but lots of concerns about the way the company is going and privacy. It doesn’t bother me but you should read about it.
I still switch over to Kodi-running-on-a-Raspberry-Pi-3 when a guest comes over and starts reminiscing about video games from their childhood or just wants to kill some time, or when the family wants to watch sports on TV -- we've watched the Olympics, the Super Bowl, and Thanksgiving-day games, year after year, on this little Raspberry Pi. Roku's app will just give up when the HDHomerun IPTV signal hiccups, but Kodi will keep going and give you the classic screen-tear / dropped i-frame mess for a sec and then catch back up. Admittedly, the video / audio will get out of sync after an hour or two, sometimes requiring us to drop and re-open the stream. But for me, Kodi is Ol' Reliable, as opposed to whatever the Roku decided to do this year.