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We present a comparative test of four widely used full spectral fitting codes, with the aim of answering the question: how robust is the retrieval of the stellar initial mass function (IMF) and other stellar properties of galaxies? We used ALF, PyStaff, Starlight, and pPXF to fit a set of optical+near-infrared spectroscopic data from the Magellan telescope of the two brightest galaxies in the Fornax cluster, NGC1399 and NGC1404. By fitting the same data set with the same models, we can compare the radial trends (out to ~ R_e) of IMF slope, age, metallicity and 19 elemental abundances when allowed with the four codes. To further test the robustness of our analysis, we carried out parallel simulations by creating inputs with different star formation history (SFH) complexity. The results from simulations show that codes such as ALF and PyStaff, which both assume a simple stellar population (SSP) return greater precision and accuracy only when the underlying population is a pure SSP; however, in cases where the SFH is more complex, these codes return erroneous results. Although codes like Starlight and pPXF, which retrieve the best-fit SFH without prior assumptions, tend to produce results with greater scatter and bias, they are generally more reliable in identifying secondary components. Our analysis on the two targets shows that ALF and PyStaff, that assume an SSP, give results pointing to a single old age, a decreasing metallicity with radius and a flat super-Salpeter IMF. In contrast, Starlight and pPXF suggest the presence of a secondary component with different metallicity and IMF characteristics.