It is the nearest thing America has to a coronation: the Inauguration ceremony of an incoming US president may, in comparison to the sacred pageant at Westminster Abbey, be somewhat lacking in pomp and circumstance; but since it occurs once every four years, rather than four times in a century, that is reasonable.
Yet where it differs even more notably is in the power being transferred: an American president, being both head of state and head of government, enjoys far more personal, executive power than either Britain’s head of state or prime minister. Ironically, an exercise in constitutional archaeology might well discover that the considerable power wielded by a US president ultimately derives from the royal prerogative exercised over the American colonies by British monarchs, at least prior to 1688.