This work describes the low-velocity impact behavior of composite sandwich panels with different types of auxetic (negative Poisson’s ratio) and non-auxetic prismatic core structures. Sandwich panels have been manufactured with carbon/fiber epoxy composite face sheets, polyurethane rigid foam core or 3D printed PLA plastic cellular honeycombs head (hexagonal, re-entrant, hexachiral and arrowhead). The material properties of the constituents have been determined via tensile and compression tests. The cellular core topologies have the same wall thickness and number of cells (39x4, except for the hexachiral topology). A rigid striker with a hemispherical head tip is dropped on the specimens with a speed of 2.6 m/s. Explicit finite element (FE) models are validated by the experimental results. Parametric numerical analyses using the validated FE have been carried out with different impact energies of 10, 20, 30, 40, 50, 60 and 76 J to identify the best core designs. The results show that non-auxetic cores could have advantages over the auxetic ones at small deformation (impact energy is equal to 10 J) thanks to the larger contact surface and higher thickness of the cellular structure. The auxetic core, however, provides greater impact resistance and energy absorption capability as the impact energy increases due to the larger densification and lower indentation during collapse. The arrowhead-based panels in particular possess 25%, 13% and 11% larger crash efficiency than the other samples for impacts with 50, 60 and 76 J. The hexachiral lattice provides the best performance at 10, 20 and 30 J, and also possesses advantages over the other cellular configurations (except for the arrowhead core) in the case of 40, 50, 60 and 76 J impact loading. As a result, the arrowhead and hexachiral configurations are those mostly recommended for applications involving impacts under large deformations.