The dependence of both individual and collective dynamic properties of simple liquids on the steepness of the potential cores is analyzed. Molecular dynamics simulations of liquids in identical conditions but assuming two repulsive interaction potentials with very different softness have been carried out. Two liquids at very different densities (with volume packing fractions eta=0.5 and eta=0.3) have been considered for each potential. The study of the dynamic collective properties includes the dynamic structure factor and the longitudinal and transverse current correlations. It has been corroborated that longitudinal modes associated with density fluctuations propagate up to higher wave numbers in liquids with softer potential cores. However, the propagating transversal modes in dense liquids are weakly influenced by the hardness of the potential core. Other properties such as the sound velocity in liquids at high density or the dynamic structure factor at the kinetic regime are rather insensitive to the details of the repulsive interactions. The velocity correlation functions for liquids with soft repulsive potential walls are markedly oscillatory. These oscillations are associated with the coupling of the atomic velocity to collective density fluctuations.