In this paper we reconciliate different homogenization results which describe the effective behavior of a heterogeneous material either by a strain-gradient model either by a micromorphic one. Indeed we prove that the solutions of both models are asymptotically very close when considering a loading with increasing wavelength. This result is obtained using the Fourier analysis on the tensor spaces and applies to a large class of micromorphic models. However, we provide an example of a micromorphic model that does not belong to this class and thus cannot be approximated by a strain-gradient model.