Strange particles produced in S-Au/W/Pb 200 A GeV and Pb-Pb 158 A GeV reactions are described invoking final hadronic phase space in thermal equilibrium, but allowing chemical nonequilibrium. Several sets of statistical freeze-out parameters are obtained for each system, invoking different models of dense matter. We show that only when allowing for strange and non-strange flavour abundance nonequilibrium, a statistically significant description of the experimental results is obtained. Physical properties of the fireball at chemical freeze-out condition are evaluated and considerable universality of hadron freeze-out between the two different collision systems is established. The relevance of the Coulomb effect in the highly charged Pb-Pb fireballs for the chemical analysis are discussed. The influence of explosive collective matter flow is also described.