Galadriel was much older. In The Silm she is listed as the daughter of Finarfin (which would make her Fėanor's niece), granddaughter of Finwė, and born in Eldamar. Elrond was born in ME in Beleriand and was actually Galadriel's son-in-law. He was knowledgeable in lore and healing, and was also the bearer of Vilya, the most powerful of the 3 elven rings.
Based on Galadriel having been born and living for many ages in Valinor, she probably has an edge over Elrond. But although they are both powerful in their own rights, neither has the power to resist Sauron indefinitely.
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"It's impossible to have Frodo without Sam, or Sam without Frodo. They're like two halves of one heart..."
"If your hurts grieve you still and the memory of your burden is heavy, then you may pass into the West..."
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