Over the past few years we have demonstrated the merits of diffraction tomography based on the Born and Rytov transformation using soft cylinders. In this paper we take a different perspective on the character of diffraction tomography methods. We compare the wavenumber spectra of the scattered waves based on the exact solution and on the Born approximation as a function of test cylinder parameters. We use these results to justify an approximate theoretical model for analyzing the magnitude of the model-based errors in the Born and Rytov reconstructed tomograms. Moreover, the study indicates the rapid breakdown of the Born method with increase in the cylinder parameters.