A comparison of the structural and magnetic properties of FePt nanostructures grown at different temperatures on NaCl(001) and MgO(001) substrates is presented. A strong influence of the deposition temperature on the epitaxial growth as well as on the size distribution of FePt nanostructures grown on NaCl substrates is observed. In spite of a large lattice mismatch between FePt and NaCl, a 'cube-over-cube' growth of nanostructures with a narrow size distribution was achieved at 520 K. Moreover, the growth of FePt nanostructures on NaCl(001) is not preceded by the formation of a wetting layer as observed on MgO(001). The higher degree of L1(0) chemical ordering in FePt nanostructures grown on MgO(001) accompanied by the absence of L1(0) variants with an in-plane tetragonal c-axis indicates that the tensile epitaxial stress induced by the MgO substrate is a key factor in the formation of the L1(0) phase with an out-of-plane c-axis. Superparamagnetic behavior is revealed for the FePt nanostructures grown on NaCl(001) due to their small size and relatively poor chemical order.