I do love that in Rohan culture, it seems that it's the custom for men to go out and fight and die heroically, and for women to honour their sacrifice by crying over their bodies or at their funerals. The men are to be brave, the woman to be loving. The men are to do great things. The women are to remember.
But in the film, whereas Eowyn's most iconic moment is her slaying of the Witch King, a great, heroic deed that cements her place in history, Eomer's most iconic moment is (arguably) his guttural scream when he sees Eowyn dead on the ground, dropping to his knees and cradling her to his chest.
Not only is Eowyn's most iconic moment a scene in which she takes on, by her culture's definition, the man's role, the most important role of a man, to die heroically, Eomer's most iconic moment is when he takes on the "woman's" role, to grieve.
I do love his "Death!" charge in the books so much, but because of this parallel between the siblings, I also love the film version where there is no battle for him to fight, no justice for him to wreak, there's nothing for him to do but cradle Eowyn to his chest and rock her back and forth.
