In the story "A Retrieved Reformation" by O. Henry, what are the defining characteristics of Ben Price and Jimmy Valentine?

Ben Price is the law-man that persistently hunts down the infamous Jimmy Valentine.  And, persistence is one of his defining characteristics.  He knows Valentine's style and habits, so when he hears that a bank has been robbed soon after Valentine got out of jail, he wisely concludes,

"That's Dandy Jim Valentine's autograph. He's resumed business...Yes, I guess I want Mr. Valentine. He'll do his bit next time without any short-time or clemency foolishness."

And, he goes off on the hunt.  He is persistent, following Jimmy's trail until he finds him.  Other men would have given up, or wouldn't have cared at all, but not Ben Price.  He is determined and dedicated.  And, at the end, when he lets Valentine go, he shows his merciful nature, as he lets Jimmy Valentine go.

Jimmy Valentine, though a criminal, shows some very un-criminal character traits in this story.  He is definitely clever, as he has robbed many banks in his time, and does so with efficiency and skill.  But, he is also selfless, as he decides to save little Agatha, who got stuck in the safe.  He knew that he would be ruining his life with his sweetheart, and giving up his freedom and reputation as he exposed himself as a bank-robber, but, he did it anyway, in order to save the little girl.  He is very responsible, considering his criminal status.  After he breaks into the safe, he sees Ben, and doesn't run.  He accepts his fate, takes responsibility for his actions, and tells Ben,

"Got around at last, have you? Well, let's go. I don't know that it makes much difference, now.”

He is willing to turn his life over to Ben, and to prison, to pay for his crime.  So, he is responsible and willing to take punishment for his actions.  I hope that those thoughts help to get you started; good luck!