Heteroepitaxial growth of BaSnO3 and Ba1−xLaxSnO3 (x = 7%) lanthanum doped barium stannate thin films on different perovskite single crystal (SrTiO3 (001) and SmScO3 (110)) substrates has been achieved by pulsed laser deposition under optimized deposition conditions. X-ray diffraction measurements indicate that the films on either of these substrates are relaxed due to the large mismatch and present a high degree of crystallinity with narrow rocking curves and smooth surface morphology while analytical quantification by proton induced X-ray emission confirms the stoichiometric La transfer from a polyphasic target, producing films with measured La contents above the bulk solubility limit. The films show degenerate semiconducting behavior on both substrates, with the observed room temperature resistivities, Hall mobilities, and carrier concentrations of 4.4 mΩ cm, 10.11 cm2 V−1 s−1, and 1.38 × 1020 cm−3 on SmScO3 and 7.8 mΩ cm, 5.8 cm2 V−1 s−1, and 1.36 × 1020 cm−3 on SrTiO3 ruling out any extrinsic contribution from the substrate. The superior electrical properties observed on the SmScO3 substrate are attributed to reduction in dislocation density from the lower lattice mismatch.