We perform a theoretical study of light propagation properties in two-dimensional square photonic crystals following Bravais-Moiré patterns, paying particular attention to the influence of the transversal shape and the orientation of the dielectric scatters onto the width and position of photonic band gaps. In this sense, we have considered both square and triangular transversal geometries for the dielectric scatters, together with the possible rotation of either all the elements or of one half of them, within the unit cell. Results for the photonic dispersion relations and band gaps are compared with those arising from the analysis of structures with simple bi-atomic Bravais unit cells. It comes out that wider photonic gaps appear when using square-shaped scatters. The use of Bravais-Moiré cells with the same kind of cores enhance the width of these gaps but shift them towards higher frequencies. Rotation of all elements within the cell in angles of 0.23 rad and 0.46 rad causes very small, if not null, changes in the photonic gap widths. However, the rotation of one half of the scatters in the cell, leaving the other half unrotated does produce noticeable modifications in the photonic band structure: For crystals made of square-shaped dielectric cores and simple cubic cells, this rotation strongly modifies the photonic structure, whilst for Bravais-Moiré crystals the same kind of change takes place for cells made of triangular-shaped cores. © 2020 Elsevier B.V.