I would tend to disagree somewhat with your implication that a Romantic writer would necessarily have dealt much differently with the events that constitute Crane's story.

Romanticism was a large-scale artistic movement with many different characteristics. Lord Byron, who is generally considered an archetypal and iconic Romantic poet, incorporates a war episode in his Don Juan epic that is realistic and even cynical in a manner similar to Crane's "An Episode of War." Crane's basic message, here and in The Red Badge of Courage, is that the ordinary soldiers and field officers do not understand the overall plan of battle and that they can only see the local things that affect them directly. The lieutenant is wounded, goes to the rear for treatment, and sees the commanding officers and messengers "as in an historical painting." To men in battle, there is something unreal about war—not the actual fighting and death, of course, which are all too real, but the higher-level plans, the "reason" for all this carnage. Not only Byron, but other writers such as Leo Tolstoy, who preceded and influenced Crane, depicted the soldier similarly, as a victim of the overall system of warfare controlled by the leaders. Much of the Romantic movement is itself pessimistic and sees man as a victim, alone in a hostile world.

One could nevertheless argue that a Romantic, rather than a Naturalistic writer such as Crane, would have embellished the war episode with a description of the lieutenant's deeper, more personal feelings, and would have placed the episode in an explicit context about man's place, either positive or negative, in a fateful universe. Crane does not provide such elaboration or commentary, but lets the facts of his tale speak for themselves. The reader is thus free to draw his or her own conclusions as to the "meaning" of all of it—if any.

In Stephen Crane's "An Episode of War," a Civil War lieutenant is shot and wounded while he is engaged in the peaceful activity of dividing coffee into rations for his troops.  

Throughout the rest of the story, no one, including the Lieutenant himself, knows how to react to the incident or how to interpret it.

*"[The soldiers'] were fixed on the mystery of [the] bullet's journey.

*"Well men shy from this new and terrible majesty [of a wound]. It is as if the wounded man's hand is upon the curtain which hangs before the revelations of all existence--the meaning of ants, potentates, wars, cities, sunshine, snow, a feather dropped from a bird's wing; and the power of it sheds radiance upon a bloody form, and makes the other men understand sometimes that they are little."

*"[The Lieutenant]  wore the look of one who knows he is the victim of a terrible disease and understands his helplessness."

*"The lieutenant hung his head, feeling...that he did not know how to be correctly wounded."

The author's attitude is that mankind is very small and insignificant in the universe, and that we cannot hope to understand the events that seem to befall us randomly.  

By contrast, an author of the Romantic movement would have emphasized the the importance of the individual hero, including the importance of his inner thoughts, feelings, and dreams.  

In a Romantic version of "An Episode of War," the Lieutenant might have heroically revenged his wound.  At the least, he would have been inspired by his experience to reach a greater and clearer understanding of life.

In the hands of the pessimistic Stephen Crane, however, the Lieutenant's arm is amputated and he returns home, none the wiser for his unfortunate accident.