[Formendacil]

To go back to Tolkien's Fëanor statement, which the Phantom so eagerly supplies, one can see that Tolkien is NOT saying that Fëanor was the greatest craftsman (and so greater than Lúthien) but that he was the greatest all around- and then lists several fields as examples.

Since Tolkien elsewhere makes a similar (although without examples) statement about Lúthien being the greatest- and since he also makes a statment lumping the two of them together with Galadriel as the greatest, it is clear that they are both great, that one of them is the greatest- and that Tolkien's word, alone and by itself, cannot be taken as the final authority.

One must therefore, to determine which is the greater, take a look at the achievements and accomplishments- and failures- of the respective Elves to decide who is the greater.