The first and most obvious difference between Elizabeth Bates ("Ordour of Chrysanthemums") and Josephine ("The Daughters of the Late Colonel") is that Elizabeth is a wife and mother whereas Josephine is a spinster (never married, never having borne children). Another difference between the two is that the dead man in Elizabeth's life is her husband Walter, whereas in Josephine's life the dead man is her father.
A similarity between the two women is that the deaths of the men in their lives brings a unasked for opportunity to look into their own lives and hearts. Elizabeth recognizes that despite Walter's irresponsible drinking--which must hold most of the cause for their failed marriage--she is not free from blame in the failure. She realizes she was never able to understand Walter; it might be argued that it is impossible to understand a man who sacrifices his dignity and the provision of his responsibilities for alcohol. Josephine realizes she can touch freedom and liberty of spirit now that her father is dead. This is revealed in how she and her sister respond to the sound of the organ grinder's music coming in through the window.