Technically (again) the British
monarch is the head of the British government (hence the term Prime
Minister). Conversely(?), the President is arguably not
the head of the American government, either, as their are three branches, and the executive is supposed to be the weakest. Therefore, collectively, Congress is the head of the government, though the President is obviously the most powerful single, elected official.
And then there's the sovereign nation made of sovereign states thing, and which is more powerful: the federal or state governments?