Higher order: Gandalf or Balrog(s)

[Earendilyon]

Gnadalf and the Moria Balrog were of the same 'order': the were both Maiar. As Maiar were Ainur, they were both "Children of Eru's Thoughts". The Maiar were less powerfull Ainur, the Valar the more powerfull. Many Maiar were corrupted by Morgoth into his service. Mightiest of them was Sauron. Others became Balrogs, because they were already spirits of fire. Some say that Maiar also inhibited the Dragons.
In the end, Gandalf proved to be more powerfull than the Moria Balrog (affectionatly known as Harry, btw). I don't know whether Gandalf the White would be more powerfull than Sauron; he himself thinks he isn't. Besides that, he was not allowed to use his full power in Middle Earth. So, even if he were more powerfull than Sauron, he was not allowed to fight him face to face. He had to get the peoples of ME to stand up against Sauron and to try to defeat him.