Gandalf is like the Tolkein version of an angelic being though, a Maiar. He's not actually mortal, although he is given mortal form when in middle earth, hence the reincarnation after the balrog fight.

Gandalf and the balrog (known as 'durins bane') are actually both Maiar, the same level of being. Balrogs are angelic servants of Melkor, aka Tolkein's answer to Satan, a rogue Ainur who refuses to serve Eru Illuvatar (Tolkein's capital G God). Gandalf is an angelic servant of Eru Illuvatar, through other members of the Ainur.

All of this considered, I really don't think there's a contest between Gandalf and Dumbledore. Old Dumbledore is a headmaster, and certainly past his prime, whereas Gandalf has existed more or less since the dawn of time itself in varying forms, is a metaphysical angelic god being in the shape of a man, and serves the creator of the entire Tolkein universe.