An extension of the folded Yukawa potential, surface and Coulomb energies formulae for the fusion of heavy ions (or fission fragments) with different charge-to-mass ratio is presented. One also has to add the volume contribution to the deformation energy. For various combinations of nuclei along the Green approximation of the line of beta stability, the general trends in the variation of interaction barriers, fusion Q values and fission barriers are studied, showing that errors of the order of some tens of MeV could appear if the difference between charge densities is ignored. Calculated interaction barriers are in good agreement with available experimental data for some 58 pairs of colliding nuclei. PES for the reactions 109Ag+40Ar, 84Kr+65Cu, 75As+74Ge, 138Ce+57Fe, 144Nd+61Ni, 116Cd+84Kr and 142Nd+84Kr are computed using the parametrisation of the asymmetric spheroid with neck. The relative values of the saddle-point energies for a real system and for a charge-equilibrated one show how important this effect could be in the entrance channel of a fusion reaction.