I've often thought of trying Plex but must confess to be completely confused about what you have to pay for and what's free, and can I live without the monthly annual subs too? Perhaps we need someone with the knowledge to start an **** Official Plex **** thread.
Plex is an offshoot of Kodi (back when Kodi was called XBMC). This is usually the reason people compare the two as they come from the same code base.
Plex's main aim in the beginning was to solve a basic problem that a lot of people had with XBMC - the lack of a central repository for your videos (and associated meta data e.g. boxart images) and a synchronised database of what you had watched.
While XBMC did support this with a couple of workarounds (setting up your own MySQL database) Plex aimed to make this as simple as possible for people.
To do this, Plex uses a "server/client" architecture.
These two parts are called "Plex Media Server" and "Plex Home Theater" and can run on your PC at home.
All of this is free.
The advantage of Plex over Kodi is that because the "client" is so light weight (as the server does all the heavy lifting) Plex can be natively installed on a large number of devices - e.g. Smart TV's, android devices and even iOS devices.
Unfortunately, like many companies adopting the "app" model, you sometimes have to pay for these. The Android version (for your phone or Amazon Fire TV) costs about £3. The iOS version is the same.
Additionally, Plex also has a paid for subscription model (Plex Pass) that allows you to try out new features before their rolled out to the free users. You can pay monthly, yearly or pay a one off "lifetime" fee.
A good example of this currently you can ONLY use Plex on a games console if you are a Plex Pass subscriber.
Created at the end of 2014 is likely by the end of 2015 these apps too will be available to free users.
The additional features you get with Plex Pass is always changing as new features are developed and older ones become free.
To see everything you gain by subscribing you can read this page:
https://plex.tv/subscription/about
The best thing about Plex (and Kodi!) is that the underlying functionality that you're likely to use on a day to day basis is free.
You can quickly go and download Plex Media Server and Plex Home Theater (even on the same PC) and see if it suits your needs - so don't be afraid to try both!