Hmmm, I'm not that fussed on either character in the same way as I have huge obsessions with characters like Bilbo, Saruman, Tom and Gandalf...though both are rather interesting in their own right.
Elrond is preferable to my tastes in The Hobbit, where he comes across as more friendly and wise and part of faerie. He's a little too Authoritarian in LotR. I maintain he does have a beard though
Eowyn can be annoying in that she is given some important work to do by Theoden but wants to enact her Amazon fantasies. However she's also touchingly determined to do her bit if you look at her another way. And I'm not bothered by her settling down with Faramir, just jealous
Hmmm....