Liveblocks is a full data layer solution -- you use their JavaScript library in your client, and they run code on their servers for synchronizing standard data types like lists and key/value maps.

By contrast, Jamsocket gives you a place to deploy your own WebSocket server, which means you can write your own data layer. This give you the control to do more advanced things like enforce invariants in the data structure.

I think of it as akin to using Firebase vs. using Postgres -- there is a place for both, and Liveblocks is a solid product, it just depends how much control you want vs. how much you want to lean on a managed service.