That's an interesting question. Certainly, the natural answer is Beren because of the reason you have all stated above of Beren being enscribed on his grave.
I'm inclined to think that he's the most like Bilbo though. As a younger hobbit, Bilbo traveled around the world and had brilliant adventures. That must have been what it was like for Tolkien. Then, as Bilbo grew older, he was content to stay at home in his cozy little hobbit hole and record the story of his adventures, or to visit the Elves, his old friends, for a story and a song from them. I think that must have been very like Tolkien. As he got older, he devoted his time entirely to writing the tales of Middle-earth and other poetry and things. To me, Bilbo must have been the most like Tolkien.

Tolkien says in one of his letters that he is "a hobbit in all but size", so he would definitely be most like a hobbit, though I don't think any specific character was meant to be similar to him. Tolkien did in fact refer to his wife as his Luthien, but this would only compare their love, not the specific characteristics of each.

So I would have to say he is neither of those characters.

_________________

Sig by Legolas

"What? In riddles? No! For I was talking aloud to myself. A habit of the old: they choose the wisest person present to speak to." -Gandalf

Bilbo.
Both are writers of some sort. In fact, they wrote the same book!!! Bilbo wrote "There and back again" or "The Hobbit" and Tolkien did too.

Well, I'm pretty sure its Beren, after all that name is engraved on his grave...

Like Erkenhelm said already, I think that only refers to their love for each other, not their character.