Both men are steadfast friends, but Bob is a criminal and Jimmy is a cop.
Both Bob and Jimmy are described physically. First, Jimmy is described.
[The] officer, with his stalwart form and slight swagger, made a fine picture of a guardian of the peace
The Bob is described.
The light showed a pale, square-jawed face with keen eyes, and a little white scar near his right eyebrow
There is a stark contrast between Bob and Jimmy, yet they both came from the same place. In a way, the story is about different paths we all have. Jimmy chooses to stay behind and follow the straight and narrow, while Bob is ambitious and hopes to make his fortune. Bob actually falls into the American metaphor of going west and becoming rich. Sometimes that involved less than virtuous activities. Jimmy becomes the law, and Bob becomes the law-breaker.
Bob arrives first. Jimmy makes his way in a leisurely way. Is this because he suspects that Bob might have become less than savory over the years?
Bob seems nice enough.
"It's all right, officer," he said, reassuringly. "I'm just waiting for a friend. It's an appointment made twenty years ago. Sounds a little funny to you, doesn't it?
He kept the appointment. So did Jimmy, but Jimmy still lived nearby. It was more a stretch for Bob. Why did Bob return? It shows that he was willing to risk going back where he may be recognized, because he wanted to be faithful to his friend.
Bob describes Jimmy as a "plodder" and says he never would have left New York. Being a cop is very important to Jimmy. His “impressiveness was habitual and not for show” and he walks down the street checking doors to make sure they’re locked. He cares about his neighborhood and his role. Yet he also cares about his friend. He cannot arrest him himself, so he gets another cop to do it. He is not willing to break the law and let his friend go, but he has not the heart to arrest him himself.
O. Henry's description of Bob's face by the light of his match has a double purpose. First, it is necessary to enable Jimmy to recognize Bob as the man who is wanted by the Chicago police. Second, it gives the author an opportunity to show the reader what Bob looks like. We must remember that both these men have changed a lot over the past twenty years. They are not a couple of kids talking to each other, but men who are both approaching middle age and who have acquired great stores of "street smarts" in their respective vocations. They are two mature men standing in the same spot where they said goodbye as mere boys twenty years before. The "white scar" near Bob's right eyebrow serves a dual purpose as well. It helps to identify him as the wanted man, and it suggests that he is a tough customer who has been in fights during his years in the West.
O. Henry's description of Jimmy's manner of patrolling his beat is largely intended to show that he has been a cop for a long time. This fact has had an indelible effect on his character and personality. He has become a cop through and through, a man who is dedicated to upholding the law. The reader will not discover until the end of the story that the policeman is in fact Jimmy Wells, but the reader will have formed a strong impression of Jimmy by that time and will understand why he found it impossible either to arrest his old friend or to let his him escape from the long arm of the law. We do not know exactly how long Jimmy has been a cop, but it could have been almost twenty years. He was twenty years old when he and Bob said goodbye in "Big Joe" Brady's restaurant. That would be about the age when he would be thinking about finding good steady employment. O. Henry's description of the policeman in the opening paragraphs suggests a man who has had many years in law enforcement and is thoroughly set in his ways as well as content in his character as a uniformed cop.
Jimmy is honest and responsible. This is clear for several reasons. As a policeman, he is charged with ensuring the safety of the storefronts on his beat. Although it is rainy and clearly a night where it would be more comfortable to be inside, Jimmy walked his beat "trying doors as he went." He does this work with style and confidence, twirling his club "with many intricate and artful movements," yet he is a humble man as he is a patrolman and content with his lot in life. He is also a man of integrity. This is clear because of his actions. First, he fulfills his obligation to meet his friend Bob after twenty years; second, realizing Bob is a criminal, he arranges to have him arrested by another officer since Bob is a friend from years ago. Clearly, Jimmy takes his job responsibilities seriously. Bob even describes Jimmy is the policeman as "the truest, staunchest old chap in the world."
Bob is showy. He wears a diamond scarf pin and pulls out a watch set with diamonds. He is boastful, bragging about all the hustles he pulled out West. Bob is descibed by the narrator as egotistical because he begins bragging about his successes to the second policeman who poses as Jimmy Wells. Even so, he is also a loyal friend, made clear by the fact he returned to the site of the restaurant he and Jimmy agreed to meet at twenty years ago to see how each had fared in life.