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High visibility (0.56) neutron-based multi-modal imaging with a Talbot–Lau interferometer at a wavelength of <inline-formula><math display="inline"><semantics><mrow><mn>1.6</mn></mrow></semantics></math></inline-formula> Å is reported. A tomography scan of a strongly absorbing quartz geode sample was performed with both the neutron and an X-ray grating interferometer (70 kVp) for a quantitative comparison. Small scattering structures embedded in the absorbing silica matrix were well resolved in neutron dark-field CT slices with a spatial resolution of about 300 μ<inline-formula><math display="inline"><semantics><mi mathvariant="normal">m</mi></semantics></math></inline-formula>. Beneficial effects, such as monochromaticity and stronger penetration power of the used neutron radiation, helped to avoid the beam hardening-related artificial dark-field signal which was present in the X-ray data. Both dark-field modalities show mostly the same structures; however, some scattering features appear only in the neutron domain. Potential applications of combined X-ray and neutron multi-modal CT enabling one to probe both the nuclear and the electron density-related structural properties are discussed. strongly absorbing samples are now accessible for the dark-field modality by the use of thermal neutrons.