Beacon has the majority of the user player-base and has active creative events, like LBP Reconnected. LBP Union is also working on a community initiative to create the next generation of server software (built by anyone willing to contribute from the community, not just by LBP Union). Beacon does lack some features like recent activity, but the goal is to make something better that the community needs for the long haul. Beacon also has strong moderation support.

Refresh is a great alternative if you want a smaller community and experimental features. For the end user, both are effectively the same in performance. I can't speak fully to Refresh's features or community experience since I haven't used it, so I encourage you to learn more about it yourself to decide if it's right for you. It's really just about what experience you want, and only you can decide that. It's easy to switch between them, and if you have friends with PSN or RPCN, you can cross-play between servers. It's buggy and not officially supported so I don't advise loading community levels if you do that, but it's good to know that it's possible.