What Greenpeace says:
An incinerator does not eliminate the need for landfill. A third of what is burnt ends up as ash which has concentrated levels of pollutants in it. A further 10 - 15% can not be burnt and goes directly to landfill. The rest of the material burnt is emitted through the chimney stack in the form of extremely poisonous gases and particles. The stack is designed to spread these pollutants over a wide area but many are re-concentrated by nature and enter the food chain. Incinerators make waste less visible, but they do not solve the problem. They transform waste into pollution.
Composting and recycling on the other hand transform waste into useful raw materials. They "close the loop" by recirculating resources. For example organic waste from kitchens and gardens, when composted puts organic matter back into the earth, replacing some of the nutrients we take out. It also "sequesters" carbon helping to slow climate change and avoids the pollution of incineration.
3 bin systems now work well in many places. Kitchen and garden waste go in one bin, "dry recyclables" (glass, metal, paper, plastic, fabric etc) in another and the third, takes what is left over (very little when the system is working properly). Households are faced with a small inconvenience of putting rubbish into one of three bins, but are rewarded with a clean local environment instead of one dominated by a polluting incinerator.
Greenpeace is pressing for the rubbish left in the third bin to be dealt with by a Zero Waste policy. This policy puts into place a number of measures designed to minimise waste generation. The main one is producer responsibility legislation. In a nutshell this means that if a product or its packaging cannot be safely re-used or recycled, it becomes the responsibility of the manufacture to take it back and deal with it in an acceptable manner at their own cost. This can provide the economic impetus necessary for waste to be designed away.
