The concentration range of the stability of polar (R3c) and antipolar phases in the Bi1-xRExFeO3 (RELa - Dy) solid solutions has been determined by X-ray study of the polycrystalline samples. Both polar and antipolar phases become less stable with a decrease of the rare earth ionic radii. It is stimulated by a reduction of the rare-earth ions polarizability with a decrease in ionic radii. The antipolar phase is characterized by a weak ferromagnetic state, whereas the polar one exhibits dominantly antiferromagnetic behavior near the polar-antipolar morphotropic boundary. The local piezoelectric response decreases with increase in antipolar phase content in the mixed polar-antipolar structural state. It is suggested that the piezoelectric activity is associated with polar (R3c) phase.