The phase perturbation technique (PPT) and the Lynch variational method (LVM) are compared in the case of scalar waves scattered by one-dimensional Dirichlet-type Gaussian random rough surfaces at normal incidence. The attention is focused on surfaces whose irregularities are comparable to or larger than the wavelength. For this purpose, expressions representing the coherent scattering coefficient and the incoherent scattering cross section within the framework of the LVM are derived with no resort to the high-frequency limit. The results show that the LVM curve lies between the PPT and the Kirchhoff approximation ones and under certain circumstances the PPT and the LVM coincide for all scattering angles. It is concluded from this evidence that a considerable part of the shadowing of the scattered field is due to diffraction from irregularities which cannot be considered flat over the wavelength scale.