I would support the view that there is a huge abyss between the powers of Galadriel and those of Luthien.
Luthien is the result of the only true union of Eru's Ainur with the hroa of Arda. She is attuned to the Living Flame in a way that no Child of Iluvatar is. And a way that even no Ainu is.
Elven "magics" or powers seem to be silent and subtle and slow. The greatest actual physical feat Finrod performed was bursting his chains; this took all of his strength. The rest of the battle between Finrod and Sauron was vocal; Finrod was defeated in mind, not in body. Elves can resist change and disease, and the Calaquendi can fend against the servants of the Enemy. They can see into the hidden places, and hide things from thought. But few examples can I think of where their exhibited powers transcend the realm of thought and communication into explosive reality. This is not to say that they cannot affect the physical world with their powers; surely, Elrond cured Frodo's wounds. But wasn't a great part of Frodo's wounding in his mind - a sickness, a sliver of despair? The old wound hurts when he feels grim. Elrond did more to his mind than to his body.
But to be of Maia-blood? There are no half-Maia other than Luthien. There are no Maia described performing the actions Luthien performed. The words she spoke rang true within the nature of the world itself. It is my personal belief that in sheer "power" in Middle-earth, she surpassed even the true Maiar. A perfect person, if you like. It appears reality changed on her whim, with such an authority did she sing. Even Melkor fell before her onslaught, for a time.
Galadriel might hold Lothlorien safe with merely her mind; she might have survived many a war and made many a weighty decision. She may have many Elven subtleties; her kindred may have defeated Maiar in battle. But this does not mean that she is any kind of match for the stature of Luthien. Luthien is completely unique, while Galadriel is ... well, simply a favoured one of the house of Finwe.
When the Great Rings enhanced the "natural powers" of their bearers, I didnt consider this to mean "natural power". I believed it meant that their actual feats of prophesy, of farsight, of defence, of preparation, would be increased in potency, by virtue of the inherent abilities of the Rings. This would not allow them to simply go off and conquer the world of darkness, as Luthien was able. (In actuality, the creation of the Rings - to my mind at least - lessened the powers of their creators. This done, of course, to improve other skills that required less power and more finesse.)
As to the actual power-levels involved... I forget the quote, but Mandos or Manwe warned Feanor that even if he were thrice what he was, he should still not hope to defeat Melkor in power and stature. Yet Luthien defeated Melkor, for a time - literally defeated him with sheer skill and strength and desperation. This is not like Hurin's defiance, who simply had the steadfast resilience to retain his will; this is not like Fingolfin's dazzling combat display, who came to the Dark Enemy bearing arms. Luthien overcame his
mind. Coming to his presence a subordinate. Does this not make her more than Feanor, in stature and sheer power? Perhaps it was only because of her singular style of approach to Melkor that she won though - although I dont personally believe it
I believe Luthien was blessed.
Galadriel and Co. are probably much more interesting characters because of their flaws, but Luthien definitely takes the power-biscuit. In a fashion, her powers much more resemble those of Wizards than those of Elves. She moulds the very substance of Arda itself, rather than changing the varied perceptions of Arda that sentient beings hold.
It has just occured to me that the Istari and Luthien have much in common. Luthien, the union of Ainu with Elf; the Istari were Ainur enclosed within the hroa of Men....
<Goes off to ponder this last point>