This article establishes the effect of structure and composition on water uptake and the hydration and proton transport properties of the oxygen-deficient perovskite series BaTi1-x(In,Sc)(x)O3-x/2, with 0.2 <= x <= 0.7. The equilibrium water uptake is determined by thermogravimetry, while combining thermogravimetry with differential scanning calorimetry allows for direct determination of the materials hydration thermodynamics. Proton and oxide ion transport properties are characterized by means of ac impedance measurements up to 1000 degrees C. In general, the hydration thermodynamics of the scandates are more favorable than that of the indates and are also affected by changes in crystal structure throughout the series. The more favorable hydration thermodynamics of cubic scandates increase their proton conductivity at higher temperatures compared to their indate counterparts. In contrast to the BaTi1-xInxO3-x/2 series, the BaTi1-xScxO3-x/2 (0.5 <= x <= 0.7) materials retain their cubic structures upon full saturation by protons and show no signs of chemical instability upon exposure to 1 atm H2O(g) down to 100 degrees C. The BaTi1-xScxO3-x/2 materials with 0.5 <= x <= 0.7 may therefore find application in, for instance, steam electrolysis or similar processes involving high water vapor pressures.