Aims: Chemical compositions and other properties of planetary nebulae around central stars of spectral types [WC], [WO], and wels are compared with those of `normal' central stars, in order to clarify the evolutionary status of each type and their interrelation. Methods: We use plasma diagnostics to derive from optical spectra the plasma parameters and chemical compositions of 48 planetary nebulae. We also reanalyze the published spectra of a sample of 167 non-WR PN. The results as well as the observational data are compared in detail with those from other studies of the objects in common. Results: The central star's spectral type is clearly correlated with electron density, temperature and excitation class of the nebula, [WC] nebulae tend to be smaller than the other types. All this corroborates the view of an evolutionary sequence from cool [WC 11] central stars inside dense, low excitation nebulae towards hot [WO 1] stars with low density, high excitation nebulae. The wels PN, however, appear to be a separate class of objects, not linked to WRPN by evolution, --abridged--