Although very similar in many technological applications, graphene and MoS2 bear significant differences if exposed to humid environments. As an example, lubrication properties of graphene are reported to improve while those of MoS2 to deteriorate: it is unclear whether this is due to oxidation from disulfide to oxide or to water adsorption on the sliding surface. By means of ab initio calculations we show here that these two layered materials have similar adsorption energies for water on the basal planes. They both tend to avoid water intercalation between their layers and to display only mild reactivity of defects located on the basal plane. It is along the edges where marked differences arise: graphene edges are more reactive at the point that they immediately prompt water splitting. MoS2 edges are more stable and consequently water adsorption is much less favoured than in graphene. We also show that water-driven oxidation of MoS2 layers is unfavoured with respect to adsorption. ; Comment: 17 pages, 4 figures