We report on the structural and magnetic characterization of (110) and (001) La2/3Ca1/3MnO3 (LCMO) epitaxial thin films simultaneously grown on (110) and (001)SrTiO3 substrates, with thicknesses t varying between 8 nm and 150 nm. It is found that while the in-plane interplanar distances of the (001) films are strongly clamped to those of the substrate and the films remain strained up to well above t=100 nm, the (110) films relax much earlier. Accurate determination of the in-plane and out-of-plane interplanar distances has allowed concluding that in all cases the unit cell volume of the manganite reduces gradually when increasing thickness, approaching the bulk value. It is observed that the magnetic properties (Curie temperature and saturation magnetization) of the (110) films are significantly improved compared to those of (001) films. These observations, combined with 55Mn-nuclear magnetic resonance data and X-ray photoemission spectroscopy, signal that the depression of the magnetic properties of the more strained (001)LCMO films is not caused by an elastic deformation of the perovskite lattice but rather due to the electronic and chemical phase separation caused by the substrate-induced strain. On the contrary, the thickness dependence of the magnetic properties of the less strained (110)LCMO films are simply described by the elastic deformation of the manganite lattice. We will argue that the different behavior of (001) and (110)LCMO films is a consequence of the dissimilar electronic structure of these interfaces.