MoS2 and WS2 emerge as important materials due to their layered structure, either as molecular sheets or as onion-like inorganic fullerenes. The prominent anisotropy within the materials requires understanding of the layer stacking sequence in order to understand the difference of physical properties of these structures from the bulk materials. Traditional Rietveld refinement in this regime proves to be inadequate to describe the crystallographic structure of these fullerene particles and nanotubes since the results contradict the direct evidence by high-resolution transmission electron microscopy. Another direct method of structure analysis, known as Debye Function Analysis, is used to determine these special features in the X-ray powder diffraction. It is demonstrated that the experimental diffraction intensities are substantially distorted compared to bulk material and that line shapes and intensities are consistent with a random stacking of trigonal prismatic MS2 layers rather than a mixture of hexagonal and rhombohedral bulk phase. We compare experimental with simulated data for fullerenes of MoS2 and platelets and nanotubes of WS2 and discuss the results in relation to growth mechanisms.