Thin film properties are strongly influenced by strain and low dimensionality effects, especially when the film thickness is about a few unit cells, which corresponds to the thicknesses targeted in most of contemporary studies. In oxides, these effects are responsible for the dramatic modification of the physical properties that sometimes can change the nature of a material. Nevertheless, it is not always possible to distinguish the contribution of the strain to the changes in physical properties from the contribution due to low dimensional effects. In the present study, bismuth iron garnet Bi3Fe5O12 (BIG) is chosen to separate both effects. This material possesses, among other outstanding physical properties, the giant Faraday rotation that allows investigating films with the thickness below a few unit cells. Three series of BIG films of various thicknesses were grown on three isostructural substrates with different lattice parameters: Y3Al5O12(001), Gd3Ga5O12(001), and (GdCa)3(GaMgZr)5O12(001). The structural, magnetic, and magneto-optic properties were studied as a function of film thickness and strain. Furthermore, critical behavior of the BIG films was investigated in the vicinity of the Curie temperature. The obtained results allowed distinguishing between the low dimensional effects and the strain due to the epitaxial growth. While the size reduction is mostly responsible for the decrease of the magnetic characteristics of the films, the strain influences rather the critical thickness below which the material starts to behave as a low dimensional system.