Several metal oxydes catalyse the oxydation, including copper and iron. The latter three can be formed by coupling elementary ring structures like the former two, called the Ullmann coupling reaction. Also the Ullmann reaction of chlorinated elementary rings is strongly catalysed by copper. At the same time dechlorination and decomposition reactions also occur and are also catalysed by copper. Which reactions are preffered is mainly a matter of temperature.
Higher temperatures favour decomposition.
For each app. Iron has a strong catalytic effect for oxydation reactions, but a weaker for chlorination and Ullmann-type reactions. Many other metals have some strong effect for one reaction but no or much weaker for the others. None of them produce as much dioxins as copper and iron do. One of the alternatives for direct incineration is thermolyses, using no air in the first step.