the main difference (hence the complementarity) between XRD and ND is in the type of interaction. X-rays interact with electrons and the scattering is directly proportional to Z. Neutrons interact with the nuclei and the Z dependence is (fortunately) completely different. This results in a high penetration e.g. in metals and high scattering contrast for materials containing e.g. hydrogen.
The dipole-dipole interaction between the magnetic omoment of the neutron and that of the atom under study is strong enough that the magnetic structure can be (in several cases) unveiled.
Neutron Diffraction is great for measuring crystalline properties - sizes, order vs. disorder, see appendix of next paper :
Small Angle Neutron Scattering (SANS) can measure the nano- to meso-structure of matter, see : Nano-metrology of porous structures - I. Using neutron scattering to access pore lattice, diameter and wall parameters, by comparison with direct calculation of scattering from models of extended arrays of regular or randomised pores. J.Beau W. Webber. Physics Reports, DOI: 10.1016/j.physrep.2013.01.002
Neutron Diffraction Cryoporometry is great for measuring the quantity and structure of crystalline phases, see : Neutron Diffraction Cryoporometry - a measurement technique for studying mesoporous materials and the phases of contained liquids and their crystalline forms. J. Beau W. Webber, John C Dore. Nuclear Inst. and Methods in Physics Research, A, 586, 356-366, 2008. DOI: 10.1016/j.nima.2007.12.004
Neutrons interact with the Nuclei and not the electrons. Neutron diffraction brings information about the position of the nuclei. The electron cloud is around an Angstrom wide so the position of atoms will have that much uncertainty, but the Nuclius has a dimension of 10-15 m.The neutron diffraction is more accurate.
Neutron has a magnetic moment. It can interact with the magnetic moment of the atoms in crystals. So it can give us the idea about the magnetic structure along with the crystal structure.
Only thing is that neutrons are available in reactors and they costly machines.