A quantitative comparison between the Milne-Eddington (ME) inversion technique implemented by Skumanich & Lites and the SIR (Stokes Inversion based on Response Functions) proposed by Ruiz Cobo & del Toro Iniesta is presented. Numerical experiments are carried out to explore the capabilities and limitations of both diagnostic techniques. Such experiments consist of inversions of Stokes profiles previously synthesized in "realistic" solar atmospheric models. The results show that the ME inversion provides accurate, line-of-sight (LOS) averaged values for the input stratification of the vector magnetic field. Its greater speed compared to SIR makes it useful for quick analysis of large quantities of data (such as those currently provided by modern spectropolarimeters) if one is only interested in LOS-averaged quantities. However, the higher order description of the atmosphere used by SIR (which acknowledges variation of the thermal, dynamic, and magnetic parameters through the photosphere) allows retrieval of the stratification of all these parameters to good accuracy. This is so even in the presence of discontinuities such as those foreseen in magnetic canopies of sunspots. The trade-offs between thermodynamic and magnetic parameters observed in some ME inversions are reduced considerably in the case of SIR inversions because of the more realistic treatment of the thermodynamics in this analysis. Notably, both allow one to extract quantitative inferences of fairly weak magnetic fields (below 500 G), even when they are applied to Zeeman-sensitive lines in the visible spectrum; i.e., well below the commonly accepted limit of 500 G. The thermodynamic parameters resulting from the ME inversion are understood theoretically in terms of the generalized response functions introduced by Ruiz Cobo & del Toro Iniesta and through the concept of height of formation for inferred values proposed by Sanchez Almeida, Ruiz Cobo, & del Toro Iniesta. The present comparison and verification of the reliability of inversion methods is a natural first step toward the ongoing analysis of the three-dimensional magnetic structure of a sunspot. By using SIR (with ME results for initialization) on maps of a whole sunspot observed by the Advanced Stokes Polarimeter, we obtain maps at different optical layers (i.e., an optical tomography) of the temperature, vector magnetic field, and LOS velocity. Such a tomography will appear in subsequent papers of the present series. To illustrate fits to the observed Stokes profiles, we show here actual inversion results for three points observed within a sunspot: one within the umbra, another from the outermost parts of the penumbra, and a third from the magnetic canopy surrounding the sunspot.