Oh, you meant Arwen and Aragorn, didn't you! Yes, well, Arwen had to give up quite a bit to follow her heart... and unfortunately she wasn't entirely happy with her decision in the end (sigh).
I'm in trouble now, I just know it!
I think you have hit on the heart of one of the lessons Tolkien included in his stories. We make our choices, hopefully to do what is right, or that which is our heart's desire. But LOTR is definitely not an 'everybody lived happily ever after' fairytale. Frodo, especially, and Legolas had their lives changed unhappily for them, and all the elves realized that the destruction of Sauron would entail their exile. Arwen's acceptance of 'the gift of men', lead her to live a fulfilled life, but suffer a lonely, premature death.