Emby and Plex are probably the two most popular media resource management and playback software right now (we won't talk about Jellyfin here; after all, it shares the same origin as Emby, and if you don't want to spend money but need hardware decoding, Jellyfin is the only choice left, so there's no real need to compare them). I actually started out using Plex and bought a lifetime membership, then later started using Emby and bought a lifetime membership as well... Looking back now, it was really a huge waste of money. That's why every once in a while, I reinstall Plex to see if there are any major changes, since buying that lifetime membership cost me a fortune.
I won't go into detail about the specific user interface or hardware decoding performance, as there are already plenty of articles about that online. Here, I will just briefly talk about the differences in usage under my own environment and needs, and the reasons why I ultimately chose Emby.
Let me first briefly describe my current hardware environment. All my resources are currently distributed across 5 NAS systems: 2 QNAP and 3 XPology (custom Synology) systems. The 2 QNAP hosts store the most frequently accessed resources, such as European and American movies, Asian movies, various TV series, cartoons, etc. The less frequently accessed resources, such as documentaries, concerts, nostalgic Western movies, and nostalgic Mainland Chinese movies, are stored on the 3 XPology systems (my hardware environment is too complex, so I will write a dedicated article to introduce it in the future).

The 2 QNAP systems are:
TS453Bmini (a 4-bay NAS, but one slot is occupied by an SSD as the system drive to achieve the HDD hibernation mentioned in another article (see:NAS Series: Synology NAS HDD Data Drive Auto-Hibernation), so only 3 HDDs are inserted) + TL-D800C (an 8-bay expansion storage, fully populated with 8 HDDs)
TVS-951N (a 9-bay NAS, with five 3.5-inch slots fully populated with HDDs, and four 2.5-inch slots with 1 SSD inserted as the system drive) + 2 TR004s (4-bay storage, fully populated with 4 HDDs).
Since the most frequently accessed resources are on these 2 NAS systems (plus, unlike the XPology systems, these are official QNAP units, so power consumption and noise are indeed much better), I deployed 2 separate Emby instances on these 2 NAS systems.
Why say so much? I mainly want to explain that my subjective feelings only apply to the situation where Emby is deployed on my two specific models of QNAP NAS, and may not suit other environments. So if you have different opinions, there's no need to take it personally.
Personally, I chose Emby mainly for the following reasons:
Decoding and Transcoding Performance
I installed both Plex and Emby on the same NAS. In terms of overall performance (only talking about 2160p/x265 movies compressed from 4K UHD Blu-rays; 1080p x265 is absolutely fine as long as it's not an ultra-high bitrate...), when using the official Plex and Emby clients respectively, Emby is slightly better: when both lag, Emby lags less~. To be honest, I really don't care about decoding and transcoding performance anymore, it's all nonsense (especially now that many 4K compressed movies are HDR or Dolby Vision. If you really want to transcode, you have to enable HDR tone mapping, and transcoding means transcoding HDR as well, which is even more unrealistic). So if Emby is deployed on a standard NAS (not a high-end NAS with an expensive CPU or even a discrete graphics card), don't expect to decode or transcode 4K movies. Of course, if your media sources are all 1080p, 720p, or other non-HD formats, it's completely fine, and there is no difference between Plex and Emby, though it can only support a small number of concurrent users. Ultimately, local playback is king.
GUI Interface
This is also quite subjective. At first, I used Plex's graphical interface and didn't find anything wrong with it. Later, when I used Emby, I found it more to my taste, mainly due to the style of the metadata editing page for media resources. For example, if you want to edit the information of a TV series, Emby is very intuitive. To modify a series' information in Emby, it's very simple—you just need to select the 3 red dots in the bottom right corner of that series:

Then click "Edit Metadata":

And then you can start editing:


Simple and clear, and I really like this style. As for Plex, although the steps are similar, when changing certain things you still need to click the mouse a few times to switch tabs and so on (I don't remember the details, I haven't used it for a long time, and maybe it has changed by now), so I ultimately chose Emby. Of course, this point is not that important either.
Access User Management
This is the most important and critical reason, which is why those who sell libraries online, and even those free public servers, all use Emby: because you can directly create and manage access users locally.
Suppose you have set up a media library and want your family and friends to access it. You have the following two choices:
If it is Plex, you need to tell them to register an account on the official Plex website (they might not know how to register, so you have to patiently guide them, or do it yourself~), then have them tell you this registered account, then you invite this account and grant access permissions, and then you need them to log into their account on the official website to accept the invitation (if they don't know how to log in and accept, you have to patiently guide them, or do it yourself~), and then they can access it with their own account.
If it is Emby, you just create an account and password locally yourself, and then tell them to access it using this username and password.
Which one would you choose? That's why I switched directly to Emby, not to mention that Emby is also better in the details of login user management.
The final result of my Emby can be seen here:My Demo Site