If I recall correctly, both Arwen and Galadriel are described as being the fairest women in Middle-earth. Since I am not interested in an opinion based answer, I am instead asking for a side by side comparison of what Tolkien wrote about each character's physical appearance.
Note 1: I managed to find this on the Wikipedia page for Galadriel; the quote comes from The Silmarillion, "Of the Rings of Power and the Third Age":
Tolkien describes Galadriel as "the mightiest and fairest of all the Elves that remained in Middle-earth" (after the death of Gil-galad) and the "greatest of elven women".
Gimli certainly agrees with this sentiment:
Gimli wept openly. "I have looked the last upon that which was fairest, he said to Legolas his companion. Henceforward I will call nothing fair unless it be her gift." He put his hand to his breast.
-The Lord of the Rings, The Fellowship of the Ring, Book II, Chapter 8: "Farewell to Lorien"
A similar assessment of Arwen as the fairest in Middle-earth comes from Aragorn's dying words - of course, as Arwen's husband, Aragorn is hardly an unbiased judge of such things:
'"At last, Lady Evenstar, fairest in this world, and most beloved, my world is fading. Lo! we have gathered, and we have spent, and now the time of payment draws near.".
-The Return of the King, Appendix A, "The Tale of Aragorn and Arwen"
Can we find a source for the claim that Arwen was the fairest more reliable than a loving husband's last words to his own wife?
Note 2: For the purposes of this question, we can include anything said or thought by one of Tolkien's characters under the umbrella of "what Tolkien wrote", since he obviously wrote what the characters say and think. I realize that we can't take the things characters think and say in LotR at face value, because they may be mistaken or even lying, but this isn't something anyone has any reason to lie about. And since beauty is always in the eye of the beholder, and therefore inherently subjective, so any question regarding beauty will always rely on the opinion of those who see the object of beauty. To put it another way, Gimli may be right about Caradhras being sentient, or he may be wrong - this is an objective question and there is a right answer, but we don't know what the right answer is. But when he says Galadriel is the fairest lady in Middle-earth, he can't be wrong - the question is a subjective one, and she meets his own personal standards of beauty. To Gimli, no one in Middle-earth is as beautiful as Galadriel. By the same token, Eomer is equally right when he says that Arwen is the fairest lady in Middle-earth, because his personal standards are different from Gimli's, and Arwen better conforms to Eomer's ideal of beauty.