The nonlinear acoustic response of low-energy excitations in insulating glasses is investigated using the tunneling model. An explicit evaluation of the sound velocity shift is performed which covers the whole temperature range of recent vibrating-reed experiments. Our results are in excellent agreement with experimental findings. The comparison with recent findings on the nonlinear response in metallic glasses shows that the dynamics of the nonlinear driven tunneling system is qualitatively different for fermionic or bosonic environments. These differences are strongly reflected in the acoustic properties.