In this work, using extensive molecular dynamics simulations of several thermophysical properties, it is proposed to analyze possible relationships (in the corresponding state sense) between monoatomic fluids for which the repulsive interactions are modeled by an inverse n-power form, the Lennard-Jones 12-6 (LJ), or by an exponential one, the exponential-6 (Exp-6). To compare results between them, two possible definitions of Exp-6 potentials "equivalent" to the LJ one are proposed. In pure fluids, for a large range of thermodynamic conditions, the properties computed are the surface tension, liquid/vapor equilibrium densities, one-phase potential energy, pressure, isometric heat capacity, thermal pressure coefficient, self-diffusion, shear viscosity, and thermal conductivity. Additionally, thermodiffusion (Soret effect) has been considered in "isotopic" equimolar mixtures. It is shown that despite similarities exhibited by alike radial distribution functions, differences exist between the thermodynamic properties values provided by the LJ fluid and the two equivalent Exp-6 fluids. Nevertheless, quite surprisingly, when temperature and density are used as inputs, all three direct transport properties are shown to be nearly independent of the choice of the potential tested. Unexpectedly, these similarities hold even for thermodiffusion which is a priori very sensitive to the nature of the interactions. These results indicate that the use of an Exp-6 potential form to describe nonbonded/nonpolar interaction in molecular simulation is an alternative (more physically acceptable) to the LJ potential when dealing simultaneously with thermodynamic and transport properties. However, when only transport properties are considered (including thermodiffusion), the Exp-6 potential form should not lead to any differences compared to the LJ one.