Quasicrystals are long-range ordered materials that lack translational invariance so that the study of their physical properties remains a challenging problem. In order to study the respective influence of the local order and of the long-range order (periodic or quasiperiodic) on lattice dynamics, we have carried out inelastic X-ray and neutron scattering experiments on single grain samples of the Zn-Mg-Sc icosahedral quasicrystal and of the Zn-Sc periodic cubic 1/1 approximant. Besides the overall similarities and the existence of a pseudo-gap in the transverse dispersion relation, marked differences are observed, the pseudo-gap being larger and better defined in the approximant than in the quasicrystal. This can be qualitatively explained using the concept of pseudo-Brillouin zone in the quasicrystal. These results are compared to simulations on atomic models and using oscillating pair potentials, which have been fitted against ab-initio data. The simulated response function reproduces both the dispersion relation but also the observed intensity distribution in the measured spectra. The partial vibrational density of states, projected on the cluster shells, is computed from this model.