guys, i think there is no comparisson,, because even though eowyn could be nice and brave...., she is not an elf,and as prog said,after all she give up immortality for strider.
and we are forgeting that aragorn has been fighting for her since he was just a youngster,because elrond required him to be a

king before he could even think on her....
and not to forget that in lothlorien she gave him the promisse that she would

love him more than the dream of valinor....and to say that is really something!!!!...
i think he has never doubted....,because after all...., that is why he is fighting for,it is his reward,the most beloved prize...., his beloved one....ERU SAVE THE QUEEN!!!