Tiara: symbol of Christian unity.
Why the tiara and not the mitre?
This is what the Decree on the Bishops' Pastoral Office in the Church has to say:
"In this Church of Christ the Roman Pontiff is the successor of Peter, to whom Christ entrusted the feeding of His sheep and lambs. Hence by divine institution he enjoys supreme, full, immediate, and universal authority over the care of souls. Since he is pastor of all the faithful, his mission is to provide for the common good of the universal Church and for the good of the individual churches. He holds, therefore, a primacy of ordinary power over all the churches."
Commentary by Fr. Walter M. Abbott, S.J.: "The terms describing different levels of authority fall into three categories: (1) that of the Pope; (2) that of the college of bishops; (3) that of individual bishops in their own dioceses. The Pope in his own right has authority that is supreme - over all the churches; full - over everything pertaining to them; immediate - over all members, including bishops, without intermediary; and ordinary - by the very reason of his office (not delegated). The college of bishops, together with its head the Pope and never without him, has this same authority over the universal Church. In his own diocese the local bishop has the same power, but it is particular to a given diocese, and subordinate (as Karl Rahner put it) to the suprme authority because the universal Church as an event is manifested in a particular diocese, and the bishop embodies the universal Church whose unity is embodied in the Pope."