Thermodynamic and structural properties of an asymmetric electrolyte containing macroions with 60 elementary charges and monovalent counterions in aqueous solution at different concentrations have been studied by means of Monte Carlo (MC) simulations and molecular dynamics (MD) employing two different short-range potentials. The long-range Coulombic interactions were handled by using Ewald summation and the MC simulations were accelerated by a cluster-move technique, which was found to be two orders of magnitude more efficient for this system than the standard MC method. An effective repulsion was found to operate between the macroions at all concentrations. The electrostatic screening of the macroion repulsion by the counterions was stronger in the hard-sphere model as compared to a soft-sphere model. The origin of this difference arises primarily from the deeper macroion-ion potential in the former model. The results of the hard-sphere model have been compared with different more approximate theories such as the cell model solved by MC simulations, the cell model solved by the Poisson-Boltzmann (PB) equation, and the Derjaguin-Landau-Vervey-Overbeek (DLVO) theory. We have found that the cell model solved by MC simulations and combined with a charge renormalization approach is superior to the other simplified approaches and its predictions are in excellent agreement with the exact simulation results.