They’re both very similar, but they do have important differences.
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Plex has a sleeker UI that is better for our less tech-savvy friends and family. I don’t mind JF’'s UI, but Plex definitely wins in this department.
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Plex is easier to access from outside your home network, especially for those of us who do not have full control of our own internet. With Plex, you just open a port, specify it for Plex, and it takes care of the rest. JF on the other hand requires the user to specify the IP (or domain if you have one).
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The first two points both result in a better experience for the end user as well. I don’t need to hold anyone’s hand when I invite them to the server, they can do it on their own. JF may not be as simple for some users.
These are the reasons why I personally use Plex over JF. However, JF is still worth considering. You don’t need to pay to unlock any features, it’s all FOSS, and imo it’s more stable than Plex. It all comes down to personal preference and your situation. Hope that helps a bit!
Most people have an extra computer of some sort for these things. An old laptop or PC can run Linux very well, and most self-hostable services are not very resource intensive.