… the Ring of Adamant was in the Land of Lórien where dwelt the Lady Galadriel. A queen she was of the woodland Elves, the wife of Celeborn of Doriath, yet she herself was of the Noldor and remembered the Day before days in Valinor, and she was the mightiest and fairest of all the Elves that remained in Middle-earth… ~for finqon
When she is no longer a child, yet not quite anything more, Mithrandir bends down and cups her face in his thin hands. He peers deeply into her eyes, and then he smiles. ’There is more than just the likeness of Lúthien about you,‘ he tells her gently. ’You would have her wildness, and fire, and bitterness too.’
She keeps that under her tongue for long years, waiting to give it voice.
Her brothers wander afar with the Dúnedain sons fostered in Imladris; she is permitted only to read the letters that come later, proclaiming the death of yet another son of Númenor. Her naneth teaches her the politesse of a lady and mistress, as well as all the private efforts which feed the illusions ease and hospitality. But when her ada welcomes princes and warriors to his chambers for counsel, she is left alone, on the cold side of the doors.
So she waits, as Lúthien did in Doriath.
Galadriel summons her to Lothlórien when she is come into womanhood–there, she sits at her daernaneth’s knee and learns statecraft and prophecy in the guise of a secretary. But while she turns the head of princelings and marchwardens, none would heed Undómiel’s voice when the mightiest and fairest of her elders presides. She is humored, not heard–that much, the age has taught her to know.
A queen she was of the woodland Elves, the wife of Celeborn of Doriath, yet she herself was of the Noldor and remembered the Day before days in Valinor, and she was the mightiest and fairest of all the Elves that remained in Middle-earth.
This one’s tricky. Because Tolkien continued writing about Galadriel, and was pretty much constantly revising her story and character, we have various sort-of-contradicting descriptions of her power (for what it’s worth, the trend was that he was making her increasingly more powerful.)
The earliest-published description of her power is in the Lord of the Rings appendices, where she’s generally said to be the “greatest of elven women.” Which doesn’t technically say anything about whether she was more powerful than Gil-galad, but the implication, I think, is that there were definitely male elves stronger than her. Also in the appendices he lists Galadriel, Gil-galad, and Cirdan to be the three greatest elves of the Second Age, but he doesn’t rank them at all.
And in The Silmarillion, Galadriel is described as “the mightiest and fairest of all the Elves that remained in Middle Earth.” This description comes after Gil-galad’s death, but it’s never stated whether he had been more powerful than her. It might very well be that the elves that no longer remained in Middle Earth is more a reference to the major powers of the First Age, such as Thingol, Fingolfin, or even Luthien.
One of Tolkien’s latest and last writings about Galadriel, found in “The History of Galadriel and Celeborn”, says that she’s “the greatest of the Noldor, except Feanor maybe, though she was wiser than he.” This description pre-dates Gil-galad’s birth, but there’s - again - no indication that his presence would have changed this statement at all.
Comparing “power” is very difficult, because that word can be interpreted in so many different ways. During the Second Age, I believe that Gil-galad was much more powerful in political and military terms, but I think that Galadriel was more powerful in spiritual and “magical” terms. As for which was more powerful overall, it seems to me that Tolkien’s left that up to the readers to decide - as far as I can tell, there’s no clear, direct statement from Tolkien saying that Gil-galad was more powerful than Galadriel (or, for that matter, that Galadriel was more powerful than Gil-galad.) If I’m wrong, and I missed a quote somewhere, please let me know!
SOURCES: LOTR Appendices, The Silmarillion, Unfinished Tales (“The History of Galadriel and Celeborn”)