Line ratio diagnostics provide valuable clues as to the source of ionizing radiation in galaxies with intense black hole accretion and starbursting events, such as local Seyfert galaxies or galaxies at the peak of their star formation history. We aim to provide a reference joint optical and mid-IR line ratio analysis for studying active galactic nucleus (AGN) identification via line-ratio diagnostics and testing predictions from photoionization models. We first obtained homogenous optical spectra with the Southern Africa Large Telescope for 42 Seyfert galaxies with available Spitzer /IRS spectroscopy, along with X-ray to mid-IR multiband data. After confirming the power of the main optical ([O III ] λ 5007) and mid-IR ([Ne V ]14.3 μm, [O IV ]25.9 μm, [Ne III ]15.7 μm) emission lines in tracing AGN activity, we explored 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 μm) continuum emission larger than 50 per cent. For targets with a lower AGN contribution, even assuming a hard ionizing field from the central accretion disk ( F ν ∝ ν α , with α ≈ −0.9), these same models do not fully reproduce the observed mid-IR line ratios. Mid-IR line ratios such as [Ne V ]14.3 μm/[Ne II ]12.8 μm, [O IV ]25.9 μm/[Ne II ]12.8 μm, and [Ne III ]15.7 μm/[Ne II ]12.8 μm 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. While mid-IR line ratios are good tracers of the AGN activity versus star formation, among the combinations of optical and mid-IR diagnostics in line-ratio diagrams, only those involving the [O I ]/H α ratio are promising diagnostics for simultaneously unraveling the relative roles of AGN, star formation, and shocks. A proper identification of the dominant source of ionizing photons would require the exploitation of analysis tools based on advanced statistical techniques as well as spatially resolved data.