The high-ionization mid-IR lines, excited in the narrow-line regions of active galactic nuclei (AGN), barely affected by stellar excitation and dust extinction, trace the AGN bolometric power. We used the complete 12um sample of Seyfert galaxies, for which 100/116 objects have reliable 2-10keV observations. The [NeV] and [OIV] mid-IR lines linearly correlate with several AGN bolometric indicators (intrinsic 2-10keV and observed 14-195keV X-ray emission, compact nuclear 12um emission, [OIII]{lambda}5007{AA} line emission) in terms of both flux and luminosity. No evidence of systematic differences in these correlations is found among the Seyfert populations, including types 1 and 2 and Compton-thick and Compton-thin AGN. Nevertheless, we find that a sequence of high-to-low Eddington ratios together with strong- to-weak line excitation (traced by the [OIV]/[NeII] line ratio) encompasses from type 1 through type 2 AGN to low-ionization nuclear emission-line region galaxies, showing intrinsic differences in these three AGN populations. A positive correlation between the black hole accretion rate (BHAR) and the star formation rate (SFR) is found, but no correlation between the specific SFR and the ratio BHAR/M_BH_, simply reflecting the fact that the more massive a galaxy is, the more it is forming stars and feeding its central black hole. The JWST, just beginning operations, will allow large samples of AGN to be observed in these lines in the nearby universe (z<0.9).