Proton jump processes in the hydration layer on the iso-structural TiO(2) rutile (110) and SnO(2) cassiterite (110) surfaces were studied with density functional theory molecular dynamics. We find that the proton jump rate is more than three times faster on cassiterite compared with rutile. A local analysis based on the correlation between the stretching band of the O-H vibrations and the strength of H-bonds indicates that the faster proton jump activity on cassiterite is produced by a stronger H-bond formation between the surface and the hydration layer above the surface. The origin of the increased H-bond strength on cassiterite is a combined effect of stronger covalent bonding and stronger electrostatic interactions due to differences of its electronic structure. The bridging oxygens form the strongest H-bonds between the surface and the hydration layer. This higher proton jump rate is likely to affect reactivity and catalytic activity on the surface. A better understanding of its origins will enable methods to control these rates.