My gut feeling is that Eomer would not have fallen to the Ring. He doesn't ever seem to have the pride that Boromir does, and I think that was simply a part of Boromir's personality. Plus the fact that the need of strong warriors meant that he was very much prized in his day. His father's favouritism didn't help, either. All this does point to Boromir being the ordinary man, because his flaws are very human.
Eomer deferred to Aragorn from the beginning. "Elfstone, since the day you rose out of the northern mists I have loved you, and that love shall not fail." I don't really see unwarranted ambition or pride in Eomer. He wants Wormtongue out of the way, but to serve the King again. "Take this, dear lord. It was ever at your service." I think he would have deferred to Aragorn had he been on the quest in Boromir's place, too. Perhaps this is natural, because he is of a royal line, but of a much smaller kingdom. The kings of Rohan are like Old English kings - in some ways more like chieftains. The majesty of Gondor makes Boromir grow up with grander ideas, in a way, even though his father is only the Steward. Faramir tells Frodo how it rather bothered Boromir that his father was not king. Frodo says he always treated Aragorn with respect, but Faramir points out that they had not yet reached Minas Tirith or become rivals in her wars. And Eomer's respect and admiration for Aragorn seems to me much stronger. "Wingfoot I name you." He is clearly very moved by Aragorn's loyalty to his companions and his heroic pursuit of the orcs in an attempt to rescue them. Boromir would be moved by such things too, though ... but he didn't witness such an act ... yes, he saw Aragorn bravely protecting the hobbits throughout the quest, but he was protecting them too ... whereas it probably played a very large part in Eomer's love and respect for Aragorn.
I realise in typing this that my memories of Eomer are very much bound up with Antony Hyde's radio performance. Perhaps rather unfairly overlooked, because he can be a a little overlooked as a character, as his sister is seen as more exceptional?
Average but pure people are thr Hobbits.
I wonder how pure Lotho was in the beginning.
