What different attitudes do the two waiters express about the old man?

Even though the two waiters understand that the old man is lonely and has recently attempted suicide, the younger waiter remains unsympathetic. He himself, he says, would not want to be that old; an old man "is a nasty thing," he says, even though the older waiter points out how clean the old man is. The younger waiter is impatient because the old man is the last customer and is keeping him from going home to his wife.
The older waiter, on the other hand, is more understanding of the old man's loneliness. As he says to the younger waiter,

I am of those who like to stay late at the café . . . With all those who do not want to go to bed. With all those who need a light for the night.

Unlike the younger waiter, who has "youth, confidence, and a job," the older waiter understands the nothingness the old man faces— the sense of uselessness or used-upness that perhaps led him to attempt suicide and that causes him to stay late at the café . The older waiter understands the appeal of a "clean and pleasant" place with good light and no music.
It's not clear what the root cause of the old man's troubles might be, but the specifics of his situation are unimportant. What matters is that the older waiter is sensitive to the same sort of emotional void the old man feels. At the end of the story, for lack of a better term, the older waiter labels that void as "insomnia."

The younger waiter finds the old man burdensome, and he is unsympathetic about his suicide attempt, saying to the deaf man, "you should have killed yourself last week." He acknowledges to the other waiter that he knows the old man is lonely, but he still wants him to leave so that they can close the cafe and go home. He tells the other waiter that he wouldn't want to be old like the man, asserting "an old man is a nasty thing."
The "unhurried," older waiter seems to know more about the old man, such as that his niece was the one who cut him down during his suicide attempt by hanging. He defends the old man, telling the other waiter that the old man needs a "clean and pleasant" "well-lighted" cafe in which to drink at night. He does not see the old man as a burden and believes that staying open another hour will be a kindness that the old man deserves. The older waiter expresses empathy for the old man, while the younger waiter expresses only impatience.