I think the ending had to do with the title "No country for Old Men" The movie really wasn't really about the dude that found the money, it was about Tommy Lee Jones and Chigurh and it didn't have any heroes in it.
The only person that is left to be the hero is Tommy Lee Jones. He manages to track Chigurh down and has the opportunity to confront him. He knows he's in the room with him, he knows if he confronts him, he'll probably die. So he leaves the hotel room and retires.
This is where those conversations become important. All throughout the movie he keeps talking about how the world has changed and he doesn't want to deal with it. When he talks to the dude in the wheelchair (his uncle?) his uncle tells him how his father died a heroic death, he kept trying to get his shotgun. His uncle himself, was paralyzed in the line of duty and look at him now. Living in a shithole with cats. Those are the two possibilities he has for being a hero. So he sits on the bed, thinks about that and walks out. He can't fight the evil that's out there now because it's "No Country For Old Men"
Chigurh's ending is different. It's his world and people like him, he can kill whoever he wants. But that doesn't mean he can't be touched. He keeps talking about chance. The only man that survives a confrontation with him was the man in the store and that was decided by a coin toss. He ends up almost dying because of a random car accident, but he doesn't because chance was on his side that time.