In Lord Of The Rings: when Frodo met Lady Galadriel alone and showed her the Ring, did she really win over the temptation of the Ring? Is her power stronger than the Ring?
Later in The Hobbit series, she once again banished Sauron while holding a crystal stone. Was she that strong to do that or Sauron just pretended?
I haven't finished reading the book yet (thanks to all the movies make me lazy to finish it :D), so I don't really know what's going on in book.
The ring's power seems throughout both the books and the movies to be primarily focused on whoever wears it, or through whoever is wearing it - Sauron is diminished without it, and it influences it's wearers in various ways. This fits the themes of Tolkien's writing where magic is itself not simply a measure of direct power but rather of intimation and connection - different magic will be more or less powerful at different tasks, or circumstances, which is a much more mythological view than the current 'modern fantasy' outlook.
The situation where Galadriel refuses the One Ring is more to do with Galadriel's own despair over the failure of the elves to reform Middle-Earth than it is the ring's own (admittedly powerful) lure. The lure, and the triumph, there are more to show how the elves (and one of the greatest of the Eldar, Galadriel) feel about the decline of middle-earth, and their own weakness (and retreat to 'The West', itself having a pile of meanings from death to seeking a new life in a strange land).
As for her power overall, she is one of the oldest and most powerful of the elves, who traveled to the western lands and learned directly from the Ainur, the literal god-angels of the setting, so she is likely no small potatoes. But like all powerful figures in Tolkien's books, her power likely has limits, and is only useful under certain circumstances. It is notable that during the War of the Ring she remains in her woods and does not seek to confront Sauron - it's likely that, as his power has grown between the events of The Hobbit and the Lord of the Rings, she would lose - or whatever trick she used to blindside him in The Hobbit would not work now that he's wise to it.
So no, Galadriel is not stronger than the One Ring, simply strong enough to resist being tempted by it, which is not the same thing. She is no pushover, but is shown as weaker than Sauron's strongest powers, which are bound up inside the ring. She does, however, indicate that she could potentially control the power of the ring - something no other wearer other than Sauron can claim.
