We compare the efficiencies of deterministic molecular dynamics (MD) and Monte Carlo (MC) methods for sampling the configuration space of finite atomic systems, in both the microcanonical and canonical ensembles. By the examples of a nonlinear molecule, Ar-3, and a linear molecule, Ar-3(+), and several physical observables such as the absorption spectrum or the average kinetic energy release in unimolecular dissociation, we show that MD sampling can exhibit significant differences with respect to MC results. At low energy or low temperature, regular orbits and vanishing Lyapunov exponents prevent Newtonian MD from being ergodic. Also, a larger effect is observed because of angular momentum conservation, which is neglected in conventional MC. We show how the use of a suitable MC scheme can notably improve the ergodic properties of Newtonian molecular dynamics sampling.