The paper focuses on optimization of lightweight sandwich panels with prismatic cores subject to bending loads in the two principal in-plane directions. Comparisons are made with optimal designs of panels with corrugated cores: a limiting case. When optimized for loading transverse to the prism axis, prismatic panels outperform those with corrugated cores, especially at lower loads. In contrast, when optimized for longitudinal loading, the corrugated core panel is always superior. Both panels exhibit significant anisotropy: a deficiency mediated by optimizing jointly for both orientations. The designs emerging from joint optimizations have only slightly lower load capacity than those optimized singly, but with the benefit of equal strengths in the two principal directions. Moreover, jointly optimized corrugated and prismatic panels perform equally well. Both are competitive with honeycomb core panels, especially at high load capacities. With the additional potential for multifunctionality (notably active cooling), the corrugated panels appear to be particularly promising thermostructural elements.