Substrate-induced strains can significantly influence the structural properties of epitaxial thin films. In ferroelectrics, this might lead to significant changes in the functional properties due to the strong electromechanical coupling in those materials. To study this in more detail, epitaxial Ba0.7Sr0.3TiO3 films, which have a perovskite structure and a structural phase transition close to room temperature, were grown with different thicknesses on REScO3 (RE–rare earth element) substrates having a smaller lattice mismatch compared to SrTiO3. A fully strained SrRuO3 bottom electrode and Pt top contacts were used to achieve a capacitor-like architecture. Different X-ray diffraction techniques were applied to study the microstructure of the films. Epitaxial films with a higher crystalline quality were obtained on scandates in comparison to SrTiO3, whereas the strain state of the functional layer was strongly dependent on the chosen substrate and the thickness. Differences in permittivity and a non-linear polarization behavior were observed at higher temperatures, suggesting that ferroelectricity is supressed under tensile strain conditions in contrast to compressive strain for our measurement configuration, while a similar reentrant relaxor-like behavior was found in all studied layers below 0°C