A modern plant turns plastic into CO_2, electricity, and, often, residential heat. So, yes, that's preferable. Among the sheer ugliness and wastefulness of landfills, burning at high temperature avoids the toxic intermediates plastics give off when degrading in nature, which landfills struggle to contain.

Ash is, by definition, inert. It is the remaining mass that does not chemically react even under extreme heat. It therefore also does not interact with, for example, the human body. Plastics are all carbon/hydrogen/nitrogen/oxygen, and, to a first approximation, do not leave any ash. In reality they do, but it's extremely little and harmless.

(Physical harms can survive an incinerator, such as material giving off radiation, but those should never be in the trash)