Who is the Fiercest Fighter in Middle-Earth?

I stumbled across this article (argument?) and just had to weigh in.
Weekly Throwdown LOTR Battle Who is the Fiercest Fighter in Middle Earth?
In case you don't feel like reading the article, the question is as follows: Which of these four is the best fighter in Middle-Earth: Gandalf, Aragorn, Legolas, or Gimli?

My problem with this article is that it seems to be based entirely on the movies. If you go by the book things are a little different. To me, though, in some ways Gandalf has to be out of the running. It's not because he is absolutely amazing; it's because he is a much higher form of being than the rest--he is one of the Maiar. He also has the red ring. Comparing him even with Legolas is kind of like saying "Who's the best fighter--the archangel Michael or Sir Lancelot?" I mean, Lancelot, though a formidable knight, has issues. When you think about his very human foibles, especially all of his lady problems and that whole insanity incident, he has no chance against an archangel. So, to me, skip Gandalf altogether and look at the rest. And then it gets hard.

Who has the true heart of the warrior? Probably Gimli. He definitely wins for sheer ferocity and verve. Who can fight, track, and still be the leader who can inspire multiple races to go into what looks like certain death? Aragorn. That's pretty darn special.

But...of these four I end up settling on Legolas despite his poetic nature. Nothing scares him because he's an elf--not even the dead bother him. He's been around a long time--3000 to 5000 years, and it is to be assumed that living in Mirkwood, he has seen more than his share of fighting evil. If you read the Silmarillian (or was it the Book of Lost Tales?) you will know that he was instrumental in saving lives during the fall of Gondolin, when he was entrusted to leading the refugees to safety in the night. Unlike everyone else in the fellowship, snow is no obstacle to him and he needs no sleep. Like Aragorn, he can track, but he also can see unbelievably far into the distance. While his main weapon is a bow--a long-range weapon--in the book he wields a long knife with deadly efficiency. In the movies he becomes a dual-wielding whirl of blades that is sheer awesomeness. No, you can't throw him. But he can jump on his own, which does seem a little more reliable. To me of this bunch, Legolas is just the most versatile and the most generally useful.

However...who is the best fighter in Middle-Earth? If you take the books into consideration at all, you'll probably end up choosing Lord Glorfindel, that elf who REALLY rescued Frodo at the Ford of Bruinen with his amazing battle skills while Lord Elrond works wonders with the water from The Last Homely House. If you read the passage it is hard to make any other decision. It is a real shame that the movie makers chose to cut this glorious elf in order to give Liv Tyler a little more to do.

Finally, why is Eowyn not even on this list? After all, she was a trained warrior who defied multiple orders and rode into battle certain of death, even embracing it. She spent that battle cutting down anyone who tried to harm Theoden King and of course ended up defeating the apparently unbeatable Witch King, which turned the tide of battle and allowed the forces of Aragorn and Eomer to win the day. For sheer courage, tenacity, loyalty, and, yes, ferocity, she surely deserves consideration here. I can only come to the conclusion that she is left out because...sigh...she is a woman.