Just thinking about these two shieldmaidens, and the stark differences between them.
I think a big one is that Eowyn is a romantic, whereas Hera has no wish to marry.
Meanwhile Eowyn hungers for battle and glory, and Hera, although willing to fight, does not desire it.
Hera seems to have grown up in a time of peace, or at least her childhood seems to have been peaceful. Although she lost her mother, she was too young to remember her, she had a father, two brothers, a cousin and a motherly figure. She had constant love, affection and security. However, Helm seems to have been protective of her, so freedom was her greatest desire.
Eowyn's mother and father died at an age for her to be devastated at their loss. She then lost her uncle, her father figure, as he succumbed to Grima's enchantments, and her brother and cousin regularly left her behind. Her life was marked with violence and loss.
Meduseld was a cage, but the only people close to her leaving Meduseld were soldiers riding to battle. Freedom meant battle, because battle was what went on beyond the walls of Meduseld. Battle also meant a place in the histories, a chance to be remembered. Battle was where her brother and cousin went when they left her behind. Battle was the opposite of the dry nursing role she was ill suited for, yet had thrust upon her.
Eowyn yearned for battle. She yearned for love. To ride to battle, to be loved, to be remembered, would ease her grief over being left behind, abandoned by those around her. Her infatuation for Aragorn was wrapped up in her admiration a soldier has for a captain. Romantic desire and desire for battle were intertwined.
Both of them were royal shieldmaidens who chafed under the expectations of their sex, and showed great courage in times of crisis, but the similarities begin and end there. Hera, we see, was playful, young, naïve, clever but sheltered, until the events of the film forced her to grow up. Hers was a coming of age story.
Eowyn was cold, despairing, bitter and angry. The events of the movie and the books see her regain the capacity for hope that was taken from her.