Part of what makes this story by O. Henry work is the parallelism of the two characters as each tries to demonstrate his or her love to his or her spouse by giving the best possible Christmas present. Each gives up the possession of greatest importance to him or her in order to purchase something that would enhance the other's dearest possession. The beauty of the message is that their love for each other is equally matched. However, there is a sense in which Della's sacrifice was incrementally greater than Jim's. While Jim pawned a family heirloom that meant a lot to him, Della actually gave a part of herself, her hair. Della's hair was a part of her identity to a greater degree than Jim's watch was a part of his. Jim kept his watch in his pocket, and although he knew it was there, others would not know about it unless he pulled it out. Della's hair, on the other hand, was visible to everyone anytime they saw her. So one reason to tell the story from Della's perspective is that her choice was more difficult and more life-changing than Jim's.
Another reason to tell the story from Della's point of view is that women are, generally speaking, known for being more emotional than men, and telling the story from Della's perspective allows O. Henry to incorporate more pathos into his tale. Della cries and worries about how Jim will react to her new look. Jim's reactions are more reserved. Instead of sobbing, "Jim tumbled down on the couch and put his hands under the back of his head and smiled." A story written from Jim's perspective could be interesting and poignant as well, but it would not have the highs and lows of emotion that the story had when told from Della's perspective.