The main parameters of the tunneling barrier of the Josephson junctions Nb/AlO_x/Nb and Nb/AlN/Nb were estimated using the Simmons method in a wide range of current densities. The dependences of the height and width of the tunnel barrier on the resistivity for each type of junctions are experimentally determined. A decrease in the height of the AlN tunnel barrier by 0.3 eV, compared with the oxide one, makes it possible to obtain junctions with a current density above 15 kA/cm² at a technologically achievable insulation layer of the order of 10 Angstroms, which makes it possible to realize the quality parameter R_j/R_n not lower than 25.