Naturally occurring cellulose Iβ with its characteristic parallel orientation of cellulose chains is less stable than cellulose II, in which neighboring pairs of chains are oriented antiparallel to each other. While the distinct hydrogen-bond patterns of these two cellulose crystal forms are well established, the energetic role of the hydrogen bonds for crystal stability, in comparison to the van der Waals (vdW) and overall electrostatic interactions in the crystals, is a matter of current debate. In this article, we investigate the relative stability of celluloses Iβ and II in energy minimizations with classical force fields. We find that the larger stability of cellulose II results from clearly stronger electrostatic interchain energies that are only partially compensated for by stronger vdW interchain energies in cellulose Iβ. In addition, we show that a multipole description of hydrogen bonds that includes the COH groups of donor and acceptor oxygen atoms leads to consistent interchain hydrogen-bond energies that account for roughly 70% and 75% of the interchain electrostatics in celluloses Iβ and II, respectively.