We have collected photometric and spectroscopic data on planetary nebulae (PNe) in 5 galaxies: the Milky Way (bulge), M31 (bulge), M 32, the LMC and the SMC. We have computed the abundances of O, Ne and N and compared them from one galaxy to another. In each Galaxy, the distribution of oxygen abundances has a large dispersion. The average O/H ratio is larger in the M31 and the Galactic bulge PNe than in those in the Magellanic Clouds. In a given galaxy, it is also larger for PNe with [OIII] luminosities greater than 100L_{sun}_, which are likely to probe more recent epochs in the galaxy history. We find that the M31 and the Galactic bulge PNe extend the very tight Ne/H-O/H correlation observed in the Galactic disk and Magellanic Clouds PNe towards higher metallicities. We note that the anticorrelation between N/O and O/H that was known to occur in the Magellanic Clouds and in the disk PNe is also marginally found in the PNe of the Galactic bulge. Furthermore, we find that high N/O ratios are higher for less luminous PNe. In M 32, all PNe have a large N/O ratio, indicating that the stellar nitrogen abundance is enhanced in this galaxy. We have also compared the PN evolution in the different galactic systems by constructing diagrams that are independent of abundances, and have found strikingly different behaviours of the various samples. In order to help in the interpretation of these data, we have constructed a grid of expanding, PN photoionization models in which the central stars evolve according to the evolutionary tracks of Bloecker (1995A&A...299..755B). These models show that the apparent spectroscopic properties of PNe are extremely dependent, not only on the central stars, but also on the masses and expansion velocities of the nebular envelopes. The main conclusion of the confrontation of the observed samples with the model grids is that the PN populations are indeed not the same in the various parent galaxies. Both stars and nebulae are different. In particular, the central stars of the Magellanic Clouds PNe are shown to evolve differently from the hydrogen burning stellar evolutionary models of Bloecker (1995). In the Galactic bulge, on the other hand, the behaviour of the observed PNe is roughly compatible with the theoretical stellar evolutionary tracks. The case of M31 is not quite clear, and additional observations are necessary. It seems that the central star mass distribution is narrower for the M31 PNe than for the Galactic bulge PNe. We show that spectroscopy of complete samples of PNe down to a factor 100 below the maximum luminosity would help to better characterize the PN central star mass distribution.