The aerospace, automotive, and marine industries are heavily reliant on sandwich panels with cellular material cores. Although honeycombs with hexagonal cells are the most commonly used geometries as cores, recently there have been new alternatives in the design of lightweight structures. The present work aims to evaluate the mechanical properties of metallic and polymeric honeycomb structures, with configurations recently proposed and different in-plane orientations, produced by additive and subtractive manufacturing processes. Structures with configurations such as regular hexagonal honeycomb (Hr), lotus (Lt), and hexagonal honeycomb with Plateau borders (Pt), with 0°, 45°, and 90° orientations were analyzed. To evaluate its properties, three-point bending tests were performed, both experimentally and by numerical modeling, by means of the finite element method. Honeycombs of two aluminum alloys and polylactic acid were fabricated. The structures produced in aluminum were obtained either by selective laser melting technology or by machining, while polylactic acid structures were obtained by material extrusion using fused filament fabrication. From the stress distribution analysis and the load–displacement curves, it was possible to evaluate the strength, stiffness, and absorbed energy of the structures. Failure modes were also analyzed for polylactic acid honeycombs. In general, a strong correlation was observed between numerical and experimental results. The results show that the stiffness and absorbed energy increase in the order, Hr, Pt, Lt, and with the orientation through the sequence, 45°, 90°, 0°. Thus, Lt structures with 0° orientation seem to be good alternatives to the traditional honeycombs used in sandwich composite panels for those industrial applications where low weight, high stiffness, and large energy-absorbing capacity are required.