Outside of your home network, Pro is required to stream your media. That is either with MediaBrowser, or using an Android device and the ServiiGo app. Within your network, Serviio makes your media available on any DLNA compliant player. This includes most Smart TVs and Blu Ray players, streaming players such as Roku or Fire TV devices, or even to your smartphone or tablet that is connected via WiFi to the same network your Serviio computer is on. The free version does this without issue.
Plex is just another type of media server. It offers both DLNA and proprietary services. Most Smart TVs have a Plex app, as does Roku Fire TV, and all forms or Android streaming players. I use Plex for when I travel, as my Roku can connect via the hotel WiFi. It's easier than connecting my laptop to the hotel TV and using MediaBrowser. I'd have to get up and made the changes on the laptop, instead of lying on the bed with the Roku remote.

But for my home network use, I far prefer Serviio for several reasons. Plex offers no user control of their device profiles, while Serviio has a single Profiles file that can be tweaked, and even supports a user-created profiles file that won't get replaced or deleted with an update. Plex has a bunch of separate profile files, and it's difficult to determine which should be modified for what you want to change. Plex doesn't support PLS or M3U playlists. Plex will not play one movie after the other without stopping (it will do that for TV shows). In my home, that's a deal breaker.

But I'm honestly not bad-mouthing Plex. It's a good product, and serves many people well. For me, Serviio is simply a more satisfying product.
Disclaimer: while I did author the Roku profiles included with Serviio, and do serve as a moderator here on the forum, I do not work for or receive any payment from Serviio. I simply support the developer of this product.