(Abridged) The chemical behaviour of an ample sample of PNe in NGC6822 is analyzed. Spectrophotometric data of 11 PNe and two H II regions were obtained with the OSIRIS spectrograph attached to the Gran Telescopio Canarias. Data for other 13 PNe and three H II regions were retrieved from the literature. Physical conditions and chemical abundances of O, N, Ne, Ar and S were derived for 19 PNe and 4 H II regions. Abundances in the PNe sample are widely distributed showing 12+log(O/H) from 7.4 to 8.2 and 12+log(Ar/H) from 4.97 to 5.80. Two groups of PNe can be differentiated: one old, with low metallicity (12+log(O/H)<8.0 and 12+log(Ar/H)<5.7) and another younger with metallicities similar to the values of H II regions. The old objects are distributed in a larger volume than the young ones. An important fraction of PNe (>30%) was found to be highly N-rich (Type I PNe). Such PNe occur at any metallicity. In addition, about 60% of the sample presents high ionization (He++/He >= 0.1), possessing a central star with effective temperature larger than 10^6 K. Possible biases in the sample are discussed. From comparison with stellar evolution models by A. Karakass group of the observed N/O abundance ratios, our PNe should have had initial masses lower than 4 M_sun, although if the comparison is made with Ne vs. O abundances, the initial masses should have been lower than 2 M_sun. It appears that these models of stars of 2-3 M_sun are producing too much 22Ne in the stellar surface at the end of the AGB. On the other hand, the comparison with another set of stellar evolution models by P. Venturas group with a different treatment of convection and on the assumptions concerning the overshoot of the convective core during the core H-burning phase, provided a reasonable agreement between N/O and Ne/H observed and predicted ratios if initial masses of more massive stars are of about 4 M_sun.
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