In the Eastern Orthodox Churches, the title is used variously. In the Greek Churches archbishops are ranked above metropolitans in precedence, as in the case of Archbishop Demetrios of America, who is the Primate of the Greek Orthodox Archdiocese of America, and primates of local churches below patriarchal rank are generally designated as archbishops. The reverse is true for the Slavic Churches (Russian Orthodox, Bulgarian Orthodox, etc. with exception of Serbian Orthodox Church and Macedonian Orthodox Church where Archbishop is ranked above Metropolitans) and for the Romanian Orthodox Church, where metropolitans rank above archbishops and the title can be used for primatial sees as well as important cities.
In neither case do metropolitans have any special authority over other ruling bishops within their provinces. However, metropolitans (archbishops in the Greek Orthodox Church) are the chairmen of their respective synods of bishops, and have special privileges.http://en.wikipedia.org/wiki/Metropolitan_bishop Archbishops and Metropolitans
The title of archbishop or metropolitan may be granted to a senior bishop, usually one who is in charge of a large ecclesiastical jurisdiction. He may or may not have provincial oversight of suffragan bishops. He may or may not have auxiliary bishops assisting him.
In the Slavonic and Antiochian traditions, a metropolitan outranks an archbishop. The reverse is the situation in the Greek tradition. The Antiochian tradition also uses the style metropolitan archbishop to differentiate from metropolitan bishops in the Greek tradition.
The change in the Greek tradition came about in later Greek history, because the diocesan bishops of ancient sees (which in the Greek diaspora include most) came to be styled metropolitans, short for "metropolitan bishops."
The Slavonic and Antiochian churches continue to follow the older tradition, where an archbishop is a senior bishop in charge of a major see, and a metropolitan is a bishop in charge of a province which may include a number of minor and/or major sees.
In the Greek tradition, all diocesan bishops of autocephalous churches such as the Church of Greece (the bishop of Patras being Metropolitan) are now metropolitans, and an archbishop holds his title as an indication of greater importance for whatever reason. The Greek Orthodox Archdiocese of America is the notable exception in the Greek practice where diocesan bishops carry the title of metropolitan. In other churches under the jurisdiction of the Ecumenical Patriarchate such as the Greek Orthodox Archdiocese of Australia the ruling bishop is the archbishop while the other bishops are auxiliary bishops with titles of the ancient sees.Non-ruling bishops
A bishop who does not rule his own diocese is either a Patriarchal Vicar or an Auxiliary Bishop. http://orthodoxwiki.org/Archbishop
If this information is not correct maybe Fr. HLL will be willing to correct it.