= Solution
Both <neutron diffraction> and <X-ray diffraction> use <interference> from atomic arrangements. <Elastic scattering> gives reciprocal-space peaks when the <momentum transfer> matches a <reciprocal lattice vector>. For a basis with sites $\mathbf r_j$, the structural amplitude is $F(\mathbf Q)=\sum_jb_j(\mathbf Q)e^{i\mathbf Q\cdot\mathbf r_j}$, and peak intensities constrain positions, occupancies and thermal displacement as well as lattice symmetry. Powder averaging loses some directional information that a suitable single-crystal measurement retains.
X-rays couple primarily to the <electron> distribution. Their atomic form factors generally favor heavier atoms and decrease with increasing scattering angle; the <wavelength> can also be tuned near an <absorption edge> for element-sensitive anomalous contrast. Neutrons scatter from nuclei with scattering lengths that vary irregularly with element and <isotope>. This can make light atoms visible beside heavy ones, and <isotope> substitution can change contrast without changing the nominal chemical element. In particular, replacing <hydrogen> with <deuterium> changes the balance of coherent and incoherent neutron scattering.
Neutron magnetic scattering also couples to electronic magnetic moments, allowing <magnetic order> to produce peaks distinct from the nuclear structure. X-ray magnetic scattering is possible too, especially under suitable resonant conditions; it is incorrect to say X-rays can never probe <magnetism>. Neutron experiments often require larger samples and dedicated sources, whereas X-ray scattering is available in laboratories as well as synchrotrons. Absorption, multiple scattering, texture and instrumental resolution affect both methods. Their complementarity comes from different contrast weights and magnetic sensitivity, rather than from two identical pictures of the same density.
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