The empirical MILES stellar library is used to test the accuracy of three different, state-of-the-art, theoretical model libraries of stellar spectra. These models are widely used in the literature for stellar population analysis. A differential approach is used so that responses to elemental abundance changes are tested rather than absolute levels of the theoretical spectra. First we directly compare model line strengths and spectra to empirical data to investigate trends. Then we test how well line strengths match when element response functions are used to account for changes in [α/Fe] abundances. The aim is to find out where models best represent real star spectra, in a differential way, and hence identify good choices of models to use in stellar population analysis involving abundance patterns. We find that most spectral line strengths are well represented by these models, particularly iron- and sodium-sensitive indices. Exceptions include the higher order Balmer lines (Hδ, Hγ), in which the models show more variation than the data, particularly at low temperatures. C24668 is systematically underestimated by the models compared to observations. We find that differences between these models are generally less significant than the ways in which models vary from the data. Corrections to C2 line lists for one set of models are identified, improving them for future use.