Rhino meshes are on ‘hard edges’ unwelded. That means that there is no connecting geometry there. A displacement map will therefor create gaps across such features.
For displacement maps to work properly you need high density meshes. The displacement mesh modifier you show on the top creates more geometry where needed in its preprocess step automatically (within the settings you give the command). This is something that a PBR material doesn’t do for you.
Low poly with render mesh shown on the left
High poly with render mesh shown on the left
