We are neither.
Special interests select representatives, citizens elect the selections. We are at least 1 remove from a republic. "A political order in which the supreme power lies in a body of citizens who are entitled to vote for officers and representatives responsible to them". -- Answers.com
We have never been an empire, although we have individuals and factions who are empire builders. In our earlier days, washington rejected being enthroned as a king, then john adams wore powdered wigs and flitted about in a royal carriage. Thanks be that t_jeff brought us back down to earth, saving us from emulating our former brit masters, a ". . . political unit having an extensive territory or comprising a number of territories or nations and ruled by a single supreme authority." -- Answers.com