Cirdan

I also am Catholic, as was the Professor. The point is well-made; in Middle-earth, for anyone to seek power as an end in itself was considered dangerous, if not evil. In the introduction to the Silmarillion, I believe, the Professor remarks that 'power' is generally used to describe the devices of the Enemy. Galadriel herself remarks on the danger of magic in the Fellowship of the Ring. But as is obvious, she never went the full distance. I would compare Luthien more to Mary, actually, in terms of purity and other qualities.

Formendacil: Amend my previous statement to read: "What female would not...Elvenesse?"

But back to the main argument: power. Someone made an excellent point about type of power. Luthien can affect the minds and wills of other people directly; Galadriel does less of this, but is more like Melian, in that her mind and will is directly engaged in conflict with the Enemy, and that she protects a land and an entire people. Luthien had no hope of contesting Sauron alone, but Sauron, by assuming werewolf-form to strive with Huan and getting owned, defeated himself. He surrendered the "words of power" for Tol-in-Gaurhoth to Luthien-the magic that held the entire fortress and its mastery. Luthien also was lucky, or wise, in that she was continually underestimated-by her father, by Sauron, by Morgoth himself.

As for deeds: Luthien holds the clear superiority. Taking a Silmaril from the Great Enemy may be the greatest single deed ever accomplished in Arda. She accomplished this, however, not through contest of power, but through charm. Essentially, she seduced Morgoth to the point where she could lay him under a spell of sleep with the excellent cloak she made. Moving into hypothesis, as goes the Dark Enemy, so go his creations. They were imbued with his power and directly tied to him; when he goes down, so do they. I don't know how else Luthien could put all of them to sleep. Again, this is not power but her natural gifts of beauty, charm, and immense courage. Galadriel had about the chance to charm someone as Carcharoth.

My last point for now is that Morgoth, though inherently far more powerful than Sauron, weakened himself, as is told in Morgoth's Ring, by pouring his energy into malice and into his creatures. By the end of the First Age, Sauron had more overall power than his master.

In terms of deeds, Luthien owns Galadriel; but when it comes to power, and the use of it, I think that Galadriel, through centuries of ruling and maintaining a kingdom against Sauron, by her natural (though Aman-enhanced) strength, deserves victory.