When comparing Lollypop vs Plex, the Slant community recommends Plex for most people. In the question“What are the best media players for UNIX-like systems?” Plex is ranked 20th while Lollypop is ranked 21st. The most important reason people chose Plex is:
It's pretty hard to find a NAS or STB that doesn't support Plex.
Specs
Ranked in these QuestionsQuestion Ranking
Pros
Pro Super intuitive way of organizing and browsing albums and artists
You can view all the albums you have in one long list. Clicking on one of them will bring a popup at the bottom of the screen where you will see a list of all the songs on that album.
Pro Works fast and reliably
Pro Super flexible layout
The latest version has a good full-screen layout and is very responsive. Goes very smoothly from full screen to minimal player (also being a GTK+ app).
Pro Integrates with the MPRIS sound menu
This applies for most players in the "Linux world", but not for all. Therefore I consider it worth mentioning.
Pro Huge development
There is constant improvements, librem and gnome3 is possibly the future.

Pro Cloud music
Lollypop allow you to play music from the web (iTunes charts and search from Spotify).
Pro Integrates well with many desktop environments
One example being the conditional use of client side decorations (a.k.a. header bars) depending on the currently active desktop environment.
Pro Good party mode
Pro Clean, light and works very well.
The only one that can play a lot of files without to stop.
Pro Queue option lets you change what's playing on the fly
You can add songs to a queue, and then re-order or remove songs as you please. It works similarly to a temporary playlist.
Pro Online radio integration
The newest version features a nice interface for adding, browsing, and playing online radio stations. This gives you access to more music than you would normally have, which can help expand your music library for free.
Pro Supported on many devices
It's pretty hard to find a NAS or STB that doesn't support Plex.
Pro Accessible via web browser
A modern web browser is enough to get everything Plex has to offer.
Pro Added lots of media databases
Metadata for media files will automatically be updated by using media databases. This provides posters, movie trailers, descriptions, information about actors, etc.
Cons
Con GTK App
Its a GTK app so integration in other desktops is terrible it also uses GNOMEs ClientSideDecorations so it will break many window managers.
Con No equalizer
Lollypop still does not have an equalizer.
Con Good party mode
Con No In-App Volume Control (0.9.242)
It has no in-app volume control, it has to be managed through system 'Sound control/Applications'

Con Requires a well organized music collection
Lollypop will be a pain to use if music is badly tagged. The setup is a one time thing, but it can be a pain to organize a large library.
Con Needs registration
You need a PLEX account even if you use it on your local LAN.
Con Proprietary software
Unfree software.
Con No gapless audio-playback
Plex still does not support gapless playback of audio files such as mp3 or FLAC.
Con Playback error: This server is not powerful enough to convert video
More hardware requirements on Plex due to a useless/non-intuitive transcoder. When using lower spec hardware (eg SBC) Plex will not transcode or play HD+ videos. When compared to other packages (eg Jellyfin which transcodes nicely using FFMeg), Plex falls short on video playback and transcode settings to get videos to play (fastest/lightest option still fails).
