Spatially resolved emission-line spectroscopy is a powerful tool to determine the physical conditions in the narrow-line region (NLR) of active galactic nuclei (AGNs). We recently used optical long-slit spectroscopy to study the NLRs of a sample of six Seyfert-2 galaxies. We have shown that such an approach, in comparison to the commonly used [OIII] narrow-band imaging alone, allows us to probe the size of the NLR in terms of AGN photoionisation. Moreover, several physical parameters of the NLR can be directly accessed. We here apply the same methods to study the NLR of six Seyfert-1 galaxies and compare our results to those of Seyfert-2 galaxies. We employ diagnostically valuable emission-line ratios to determine the physical properties of the NLR, including the core values and radial dependencies of density, ionisation parameter, and reddening. Tracking the radial change of emission-line ratios in diagnostic diagrams allows us to measure the transition between AGN-like and HII-like line excitation, and thus we are able to measure the size of the NLR. In the diagnostic diagrams, we find a transition between line ratios falling in the AGN regime and those typical for HII regions in two Seyfert-1 galaxies, thus determining the size of the NLR. The central electron temperature and ionisation parameter are in general higher in type-1 Seyferts than in type 2s. In almost all cases, both electron density and ionisation parameter decrease with radius. In general, the decrease is faster in Seyfert-1 galaxies than in type 2s. In several objects, the gaseous velocity distribution is characteristic for rotational motion in an (inclined) emission-line disk in the centre. We give estimates of the black hole masses. We discuss our findings in detail for each object.