Li3Co2SbO6 is found to adopt two highly distinct structural forms: a pseudohexagonal (monoclinic C2/m) layered O3-LiCoO2 type phase with "honeycomb" 2:1 ordering of Co and Sb, and an orthorhombic Fddd phase, isostructural with Li3Co2TaO6 but with the addition of significant Li/Co ordering. Pure samples of both phases can be obtained by conventional solid-state synthesis via a precursor route using Li3SbO4 and CoO, by controlling particle size, initial lithium excess, and reaction time. Both phases show relatively poor performance as lithium-ion battery cathode materials in their as-made states, but complex and interesting low-temperature magnetic properties. The honeycomb phase is the first of its type to show A-type antiferromagnetic order (ferromagnetic planes, antiferromagnetically coupled) below TN = 14 K. Isothermal magnetization and in-field neutron diffraction below TN show clear evidence for a metamagnetic transition at H ≈ 0.7 T to three-dimensional ferromagnetic order. The orthorhombic phase orders antiferromagnetically below TN = 112 K and then undergoes two more transitions at 80 and 60 K. Neutron diffraction data show that the ground state is incommensurate.