The Greatest Warrior...

[Legate of Amon Lanc]

Well, I of course assumed, that the words

the most capable of destroying their opponent

do not mean one particular opponent, but any opponent. You cannot say Farmer Maggot was the greatest warrior just because he was the most capable of destroying his opponent, who was a cockroach, whom he totally crushed under his foot and almost nothing remained of him. Not even Fingolfin managed to crush Morgoth into such little pieces. But generally, Farmer Maggot, nor Éowyn I believe, would be able to face, let's say, Morgoth.

Though, when we speak of it, Éowyn is a good choice. I believe she could be able to stand maybe even up to Glaurung, or Sauron (though in both cases with some difficulties, no doubt). But I don't believe she would (in contrary to my nominated champion Fingolfin) even scratch Morgoth.