On the left is the skeletal mesh does not maintain proper smoothing groups. The static mesh on the right is perfectly normal. This happens when importing skeletal meshes. Blender 2.72 and I have tried both the 6.1 and 7.4 exporters. Both of those produce the output on the left when a skeletal mesh and both of those produce the mesh on the right when only the static mesh is imported.
No combination of applying modifiers or edge smoothing on export works.