The only obvious simile in the story occurs when Bob is telling the policeman, whom he doesn't recognize as his old friend Jimmy Wells, about the strong friendship that had existed between the two youths until they parted company twenty years ago. Bob says,
He and I were raised here in New York, just like two brothers, together.
This helps to explain why Bob would have gone to so much trouble and expense to come all the way from Chicago to New York to keep a dinner date with Jimmy. They grew up together in New York but were not blood relatives. If Bob had actually been Jimmy's brother, the reader might wonder how Jimmy might have acted when he realized Bob was the man wanted by the Chicago police. Would Jimmy have turned his own brother in?
O. Henry is using the simile of "just like two brothers" for two reasons. One is to suggest that Bob's comparison will make a strong impression on the cop, which it apparently does, because Jimmy can't bring himself to make the arrest himself. The other reason O. Henry uses that simile is to impress on the reader as strongly as possible how close the two young men were twenty years ago. The reader has to understand how hard it must have been for Jimmy to double-cross his "brother," as well as to understand the emotional impact that deception and double-cross would have on Bob.