From a technical sense, Sauron and the Balrogs were Maiar, not Valar. That meant that they were designed as lesser beings from the beginning of time. Thus, in their original forms, Morgoth would have easily defeated Sauron in a fight.
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.
Morgoth was beaten by a combination of Elves, at a time when they were far greater than any of the Elves we met in Lord of the Rings, and Maia — possibly with the aid of a Vala or two. A few Men were involved as comparatively minor figures, and those were the very best that humanity ever had to offer.
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.
Additionally, while he was in his weakened state, Galadriel could hold him off through the power of will alone. 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.
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Did Galadriel defeat Morgoth?
She had no role in the major wars of the First Age, believing that defeating Morgoth was beyond the power of the Eldar; when Morgoth was defeated by the coming of the Valar out of the West she, having played no part in the earlier Kinslaying, was offered safe return to Valinor.
Melkor is the most powerful of the Valar but he turns to darkness and is renamed Morgoth, the primary antagonist of Arda. All evil in the world of Middle-earth ultimately stems from him. One of the Maiar of Aulë betrays his kind and becomes Morgoth's principal lieutenant and successor, Sauron.
Túrin will run his black sword Gurthang (Iron of Death) through Melkor's heart, thus avenging the Children of Húrin (Sindarin: Hîn Húrin) and all the fallen (In the end of The Hiding of Valinor Eönwë, and not Turin, kills Morgoth).
Gandalf pursued the monster for eight days, until they climbed to the peak of Zirakzigil, where the Balrog was forced to turn and fight, its body erupting into new flame. Here they fought for two days and nights. In the end, the Balrog was defeated and cast down, breaking the mountainside where it fell "in ruin".
It was said that Morgoth hated and feared the House of Fingolfin most among the Houses of the sons of Finwë, especially Fingolfin's son Turgon, as it was prophesied that his doom would come from the House of Turgon.
Fingolfin, receiving false news, rode alone to Angband and challenged Morgoth to single combat. He wounded Morgoth several times, but grew weary and was killed by the immortal Vala. Fingolfin has inspired artists, musicians and video game designers to create depictions of his deeds.
"So I think in his pitch to Galadriel, it cannot mean that he loves her or that there's any kind of romantic relationship. There should be no ambiguity around the fact that Sauron is evil — he's terrible, and he's using Galadriel to enhance his power."
Gandalf's main reason for supporting Thorin's quest in The Hobbit was to eliminate the threat of the dragon Smaug, who would be a powerful ally for Sauron. Despite popular belief, the Balrog known as Durin's Bane was more powerful than Smaug in Middle-earth, being a literal, primordial demon.
While Morgoth doesn't appear in The Lord of the Rings or The Hobbit, he plays a significant role in The Silmarillion and Tolkien's other writings, and his reign of terror had a far bigger impact on Middle-earth history than Sauron's — as seen in Amazon's The Rings of Power series.
After Morgoth's ousting by the Valar, Sauron became the second Dark Lord and sought to conquer most of Arda through guileful trickery, with the Rings of Power or with overwhelming armies.
For that matter, the Valar didn't have the authority to remove another Ainur's power. If they had had that authority, they would have stripped Morgoth of his power, rather than going to war with him so many times.
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. Though this would eventually corrupt Aragorn, it would allow him to destroy Sauron and take his place.
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.
Thus, Galadriel's dark form in Jackson's The Lord of the Rings personified what would have occurred had the Lady of Lothlorien given in to temptation and taken the One Ring for herself. She would have succumbed to evil because the Ring was indomitable, even with her power.
She also resisted being offered the ring of power by Frodo following his vision in the mirror of Galadriel, an immense test given the ring's seductive powers. Yet Gandalf's power level exceeds even that of Galadriel, as shown by his rebirth in the Two Towers.
