We present the second part of an optical spectroscopic study of planetary nebulae in the LMC and SMC. The first paper, Leisy & Dennefeld (1996, Cat. <J/A+AS/116/95>), discussed the CNO cycle for those objects where C abundances were available. In this paper we concentrate more on other elemental abundances (such as O, Ne, S, Ar) and their implications for the evolution of the progenitor stars. We use a much larger sample of 183 objects, of which 65 are our own observations, where the abundances have been re-derived in a homogeneous way. For 156 of them, the quality of data is considered to be satisfactory for further analysis.