Hybrid DFT model calculations have been performed for some cobalt complexes capable of oxidizing water. Since a very plausible mechanism for the oxygen-evolving complex involving the cuboidal Mn4Ca structure in photosystem II (PSII) has recently been established, the most important part of the present study concerns a detailed comparison between cobalt and manganese as water oxidation catalysts. One similarity found is that a M(IV)-O(•) state is the key precursor for O-O bond formation in both cases. This means that simply getting a M(IV) state is not enough; a formal M(V)═O state is required, with two oxidations on one center from M(III). For cobalt, not even that is enough. A singlet coupled state is required at this oxidation level, which is not the ground state. It is shown that there are also more fundamental differences between catalysts based on these metals. The favorable low-barrier direct coupling mechanism found for PSII is not possible for the corresponding cobalt complexes. The origin of this difference is explained. For the only oxygen-evolving cubic Co4O4 complex with a defined structure, described by Dismukes et al., the calculated results are in good agreement with experiments. For the Co4 models of the amorphous cobalt-oxo catalyst found by Nocera et al., higher barriers are found than the one obtained experimentally. The reasons for this are discussed.