There's a lot of great insight in that post and the comments. The phrase that's just grabbed me comes from one of recessional's comments:

"The movie just . . . lessened that, so that she became Plucky and Brave, instead of desperate and, frankly, suicidal, but clinging to the last shards of an honour that demanded her death mean something."

Something in that really gets at who Eowyn was for me. (It's possible that this sort of cheapening of all the characters was inevitable in a movie adaptation of such a long book, but it's also inevitably the biggest regret we Tolkien fans have about the project, whether we enjoyed the movies or not.)