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We present a coherent database of spectroscopic observations of far-IRfine-structure lines from the Herschel/PACS archive for a sample of 170 localAGN, plus a comparison sample of 20 starburst galaxies and 43 dwarf galaxies.Published Spitzer/IRS and Herschel/SPIRE line fluxes are included to extend ourdatabase to the full 10-600 $\mu m$ spectral range. The observations arecompared to a set of CLOUDY photoionisation models to estimate the abovephysical quantities through different diagnostic diagrams. We confirm thepresence of a stratification of gas density in the emission regions of thegalaxies, which increases with the ionisation potential of the emission lines.The new [OIV]25.9$\mu m$/[OIII]88$\mu m$ vs [NeIII]15.6$\mu m$/[NeII]12.8$\mum$ diagram is proposed as the best diagnostic to separate: $i)$ AGN activityfrom any kind of star formation; and $ii)$ low-metallicity dwarf galaxies fromstarburst galaxies. Current stellar atmosphere models fail to reproduce theobserved [OIV]25.9$\mu m$/[OIII]88$\mu m$ ratios, which are much higher whencompared to the predicted values. Finally, the ([NeIII]15.6$\mu m$ +[NeII]12.8$\mu m$)/([SIV]10.5$\mu m$ + [SIII]18.7$\mu m$) ratio is proposed asa promising metallicity tracer to be used in obscured objects, where opticallines fail to accurately measure the metallicity. The diagnostic power of mid-to far-infrared spectroscopy shown here for local galaxies will be of crucialimportance to study galaxy evolution during the dust-obscured phase at the peakof the star formation and black-hole accretion activity ($1 < z < 4$). Thisstudy will be addressed by future deep spectroscopic surveys with present andforthcoming facilities such as JWST, ALMA, and SPICA.

Far-infrared line spectra of active galaxies from the Herschel/PACS Spectrometer: the complete database