Impossible to choose! I like Éowyn's courage, but dislike her clingy side. I've always had a low threshhold for tolerating soppiness.
As for Arwen, I like her loyalty to Aragorn, but the book Arwen makes a pretty standard while others are doing great deeds and the film version has left Glorfindel tied up in a ditvh somewhere. I can't really choose her until she gives up sissy needlework and horse theft (or at least steals from someone other than Glorfindel).
I know all this is very unfair. I really do like them both, honestly! I just have this anti-romance instinct!
The following is not LotR based. It comes from my own fantasy world of Edeba, but this is my kind of heroine, and when Éowyn is thinking like this, I like her best.
A Cry For Arms.
It's true I watched the joust with eyes afire
And stayed until the ending of the fight,
But do not think that this is any sign
That this young maid has eyes for any knight.
It's true my gaze more often came to rest
Upon the armour of the northern lord,
But truly, I do not desire his heart,
The only thing I covet is his sword.
My sisters long to be among the crowds
Who for their husbands loyally must wait,
I do not want to wave a man to war
But how my heart longs to participate!
I yearn for the sweet song of blade on blade,
The battlefield with baneful sun above.
Let my heart pound with passions far more clean
Than those that torture simple souls in love.
These arms were never built to hold a babe,
Nor are these hands to needlework inclined,
But give the hand a sword, the arm a shield
And then my true vocation you will find.
No wedding ring for me to bind my heart,
Let my liege-finger bear the only ring.
Then, like these knights who jousted here today,
I'll live or die in battle for my king.
Now father, do not look so dragon-struck.
I heard you mutter, "Oh, what have I done?"
Fear not that you have lost a little girl,
But see it as the gaining of a son.
~~~~~~~~~~~~~~~~
Neneithel