Line ratio diagnostics provide valuable clues on the source of ionizing radiation in galaxies with intense black hole accretion and starbursting events, such as local Seyfert or galaxies at the peak of the star formation history. We aim to provide a reference joint optical and mid-IR analysis for studying AGN identification via line ratios and testing predictions from photoionization models. We obtained homogenous optical spectra with the Southern Africa Large Telescope for 42 Seyfert galaxies with Spitzer/IRS spectroscopy and X-ray to mid-IR multiband data available. After confirming the power of the main optical (OIII) and mid-IR (NeV, OIV, NeIII) emission lines in tracing AGN activity, we explore diagrams based on ratios of optical and mid-IR lines by exploiting photoionization models of different ionizing sources (AGN, star formation and shocks). We find that pure AGN photoionization models are good at reproducing observations of Seyfert galaxies with an AGN fractional contribution to the mid-IR (5-40 micron) emission larger than 50 per cent. For targets with a lower AGN contribution these same models do not fully reproduce the observed mid-IR line ratios. Mid-IR ratios like NeV/NeII, OIV/NeII and NeIII/NeII show a dependence on the AGN fractional contribution to the mid-IR unlike optical line ratios. An additional source of ionization, either from star formation or radiative shocks, can help explain the observations in the mid-IR. Among combinations of optical and mid-IR diagnostics in line ratio diagrams, only those involving the OI/Halpha ratio are promising diagnostics for simultaneously unraveling the relative role of AGN, star formation and, shocks. A proper identification of the dominant ionizing source would require the exploitation of analysis tools based on advanced statistical techniques as well as spatially resolved data.