Is Ultimate Member a full social network like BuddyNext?
Not out of the box. Ultimate Member is profiles-and-membership first - its core is user profiles, registration forms, directories, roles, and content restriction. Social features like private messages, groups, and follow come from separate paid extensions. BuddyNext ships the feed, spaces, messaging, and moderation as core, so a community is the starting point rather than something you assemble.
Do both keep my data on my own server?
Yes. Both are self-hosted WordPress plugins, so your members, profiles, and posts live in your own database on your own hosting. Neither puts your community on a hosted platform you do not control.
Can I just use Ultimate Member and add the social parts later?
You can - that is exactly its model. You buy the messaging, groups, and follow extensions as you need them. The trade-off is that you are then maintaining a base plugin plus several extensions and keeping them compatible. BuddyNext folds those into one integrated platform, which is simpler if you know up front you want a real community.
Which is cheaper?
It depends on how much community you need. If you only want profiles, directories, and gated content, Ultimate Member can be cheaper because you buy only the pieces you use. Once you need messaging, groups, and moderation too, the extensions add up, and a single BuddyNext Pro license that already includes those (plus the app) can come out ahead. Check current pricing on each site.
Does Ultimate Member have moderation tools like BuddyNext?
Its strengths are roles, profile approval, and content restriction rather than a member-content moderation queue. BuddyNext ships a moderation queue and safeguards in the free core, which matters once members are posting to a shared feed and to each other rather than just filling out profiles.