I want to make a game like this: https://summer-afternoon.vlucendo.com/ with collision detection.
Would Rapier.js be better performing than three-mesh-bvh for an open world multiplayer game?
In a similar way as not using three.js would be better performing than using three.js.
Rapier is physics - it will do collision detection, collision solvers, force accumulation, joints, and all the other physics magic on each frame.
three-mesh-bvh can only do collision detection for you - the rest you’d just code yourself based on what you’d need. If you need only collisions, no physics besides that - three-mesh-bvh may be faster.
But regardless of which choice you’d go with - the scale of the world should not matter. Physics and collisions should be applied only locally, to what player may see / notice on their screen - simulating physics and collisions on every tiny rock 2000km away from the player will wreck the performance regardless of the technology you’d use 
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