Sauron's deepest fear was that Aragorn would use the Ring against him. With its powers of domination, Aragorn could comfortably take over the entirety of Sauron's dark army.
In the Third Age, he probably considered Saruman as his worst enemy, until he became corrupted. And he remained a threat, seeking the One Ring for himself. But he'd then have seen Gandalf as the chief problem. Someone who constantly caused his plans to fail.
Why does Sauron fear Gandalf and not the Balrog. Sauron does not fear Durin's Bane because essentially they had been allies back “in the olden days". Both Balrogs (all balrogs) and Sauron chose to serve Melkor/Morgoth.
In his notes, Tolkien remarks that Sauron saw Galadriel as his equal. Add that to the fact that she's untrusting of Sauron (yes, even when he's in his Annatar guise) and an unwavering, single-minded force, and it's more likely than not that Sauron feared Galadriel — or the potential she held to upend his plans.
Morgoth, the first to reign terror upon Middle-earth, was more powerful than Sauron and commanded an army of dragons and Balrogs. While both Morgoth and Sauron were cunning, Morgoth's rule and terror lasted longer and his corruption spread further, making him more formidable in the Lord of the Rings universe.
Meanwhile, a few faithful Númenóreans, led by Elendil, were saved from the flood, and they founded Gondor and Arnor in Middle-earth. Sauron still considered them his hated enemies and he launched a pre-emptive attack on Gondor in S.A. 3429.
In their prime, there can be no comparison. Morgoth is the more powerful of the two. Morgoth was the mightiest of the Valar, a group whose weakest member would outpace Sauron.
Bloodlines are very important in Tolkien's stories, and it makes a lot of sense that Sauron would fear the great-grandson of the man who cut off his hand. Aragorn carried the blood of Numenor with him. His genetic connection to the heroes of the Second Age established him as a dangerous opponent of Sauron.
This is given a visual representation in the film. Rather than cast magic at Sauron, Galadriel opts to challenge him on the spiritual plane; she resorts to her Wrath form to penetrate Sauron's mind and break his will. She obviously succeeds, as Sauron audibly cries aloud as he flees.
Though wizards are technically Maiar, they do not possess all the same abilities in their wizard forms. This is why, despite Balrogs and Sauron also being Maiar, Gandalf wasn't evenly matched in his wizarding form—especially as Gandalf the Grey.
They served Sauron out of fear, but they also savored the chance to kill and feast on the other beings in Middle-earth. Orcs were vicious fighters, but they had one noticeable flaw. They absolutely despised sunlight. As servants of evil, that makes sense, but there's actually a much more lore-centric reason.
He will fight in the Last Battle against the Valar and their allies, but will ultimately be slain by Túrin Turambar, the Man he cursed. By finally defeating Morgoth, Túrin will avenge not only himself, but all members of the race of Men.
Gandalf the White is particularly good as a counter to Sauron because he can bring troops - and as was mentioned above, he doesn't need to bring yet-another-expensive-hero to the party (like Galadriel usually does).
By about SA 1500, Sauron put on a fair visage and called himself Annatar, the "Lord of Gifts". The Unfinished Tales tells that Annatar assumed the guise of an emissary of the Valar "anticipating the Istari".
Originally Answered: Why was Gandalf afraid of the Balrog of Morgoth? Gandalf knew that the Balrog of Morgoth was at least as powerful as he was. Gandalf was reluctant to display just how powerful he really was, at least at that time.
Sauron, in origin a Maia of Aulë like Saruman, awed and frightened him. During the height of his arrogance, Saruman thought he could contend with Sauron, but in the end he found himself meddling with a spirit of far greater power and knowledge than himself.
Isildur, son of Elendil, is Aragorn's ancestor who failed to destroy the Ring when given the chance. Aragorn recognizes that a sense of weakness runs in his blood, and he's subsequently terrified that he will succumb to the same fate as Isildur.
In Tolkien's The Return of the King, Sauron never fights Aragorn. In fact, Sauron's appearance is never properly described, perhaps because he's a notorious shapeshifter. As such, showing Aragorn fighting Sauron would be a disservice to the author.
Could Aragorn Have Defeated Full-Strength Sauron? The Short answer here is absolutely not, with a tiny caveat that it's possible if Aragorn got incredibly lucky as Isildur had. It's important to always have that small caveat in case Sauron's power once again returned to a similar arrogance.
Sauron was an Ainu. The Ainur were the "angels" of Eru Illuvatar and sang a song which He used as a template to create the Universe. The Ainur were then allowed to enter into the Universe.
However, if Sauron had his One Ring and faced off in a battle against Galadriel, it's unlikely that there would be much she could do. He was considered the strongest of the Maiar for a reason, and his One Ring was even more of a threat.
Finally Sauron came out to fight Elendil and Gil-galad face to face. When Elendil fell, his sword Narsil broke beneath him. Isildur took up the hilt-shard of Narsil and cut the One Ring from Sauron's hand, vanquishing Sauron.
