I thoroughly enjoyed Ragtime and Billy Bathgate and RDC liked those plus Sweet Land Stories and this, so I had high hopes. I do like it, and as an audio book it's a good companion to The Killer Angels and The Known World, combining the former's military and the latter's civilian life as it does (though World is antebellum).
Unfortunately a couple of things jarred me out of the story. In dialogue, Doctorow writes realistic speech faithfully, with "mens" and "he don't" and General Sherman saying "darkie" when better educated or less prejudiced whites say "Negro," etc. In internal dialogue, he uses such markers only occasionally in otherwise standard English, out of context. Maybe this works better in print than in audio, and maybe some of it is the performer's fault: he speaks dialogue differently than narration, but internal dialogue as narration. Another thing was anachronistic vocabulary. Although "guerrilla" originated in the early 19th century (to mean the sort of warfare the Spanish could conduct against the invading French under Napoleon; the tactics of course predated their name) and it's possible that Sherman would have used that word, it does not seem to me likely that an illiterate fieldhand like Coalhouse would know it. "Bivouac," too, I thought was an anachronism, of WWI coinage, but Etymology Online says it came into English also after the Napoleonic wars.
The March was an excellent complement to The Killer Angels and The Known World. Before reading the former, what I knew of Gettysburg was its date, that the North won and thank goodness because we desperately needed a victory for morale and public support, that the South lost because Lee made a major error, and that Lincoln made a brilliant speech. Having read it, I know more of the key players' names, and what the mistake was, and that the cherries were ripe in southern Pennsylvania. But I guess I don't need to know the exact specifics of who moved where when. The time was I could you the troop movements in Tours, Crécy, Verdun, and Normandy; that time has passed and I doubt I will ever reread The Longest Day or The Song of Roland. The Known World is antebellum and from several African-American perspectives, and wholly invented (not just fictional). The March was good in that it showed several characters' perspectives over time, free and freed, civilian and military, white and black--and how the gray are those concepts of supposed opposites.