Faramir has finally discovered Frodo's true character and motives. He could have decided Frodo's actions with the Ringwraith are yet more evidence that the hobbit is incapable of finishing his task. Surprisingly, he does not. He says: "At last we understand one another."

Frodo and Sam have been assuming he's just like Boromir, which he's not. He's more of a thinker and a philosopher. Currently, he's a very depressed young man, dealing with his brother's death and the weight of responsibility for Gondor's safety and by extension all that of Middle Earth. Faramir knows that the world is depending on him, but that he does not have the strength or resources to succeed. He, also, "cannot do this". Yet he is persisting in his mission anyway, knowing the odds to be hopeless. Frodo is evidently doing much the same thing, for the same reasons. And both of them are mourning the death of a loved one: Frodo in the movie is desperately shaken by the loss of his father figure, Gandalf, and Faramir has lost the brother he loved and admired so much.

So Faramir decides to sacrifice his own life on the slim chance that Frodo can succeed where he can't. "Then my life is forfeit." Noble and soft-spoken and brave: that's exactly what we'd expect of book-Faramir (who, incidentally, is not under a death sentence: he just said he would deserve to die if he made a decision that proved ill for Gondor). When the movie characters finally part ways, Frodo is going to Mount Doom with a duty he's been given by his superiors which — as Galadriel tells Elrond — he knows will claim his life.

Faramir is going back to Minas Tirith with a death sentence stapled to his forehead.

They do understand one another. For they are the same.

And perhaps Faramir sees in Sam, who has more hope than they do, a little of the brother he misses so much.