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This 'power' thing is a difficult question if it's limited to a question of 'force'. Certainly, there is an 'enhancement' of innate power which comes from having once dwelt in the Undying Lands - as we see with Glorfindel, who had seen the Two Trees: the Light of Aman was in his face.
Galadriel had also seen the Light of the Trees & the Light of Aman would have been in her face as well, & that Light was Holy, & evil things could not stand before it. However, unlike Glorfindel, Galadriel had never passed to Mandos to be purified of her sin in the Rebellion, so she would probably not have had his innate power sans Nenya.
Luthien, on the other hand, was the daughter of a Maiar, but had not dwelt in the West, or seen the Light of the Trees - though her father had.
More interesting, I think, is the fact that in the end, both Luthien & Galadriel reject power: Luthien chooses mortality, Galadriel to 'diminish'. Power is clearly not the be all & end all for either of them. Luthien chooses love (& mortality) over power & Galadriel to 'diminish' & go into the West, where rather than an absolute monarch she will become merely a returning penitent seeking forgiveness.
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