Are domains bigger or smaller than kingdoms?

In Biology, a kingdom is a subsection of a domain. Thus, domains are bigger than kingdoms; they are in fact the highest subdivision of biological life in general.

In other usage, a domain - sometimes demesne is used as a synonym - refers to the Area controlled by a group or an individual. As such, a domain would almost always be smaller than a kingdom, but kingdoms themselves are the domain of a king, and in that case would make neither larger than the other.