I find the Red River Campaign fascinating for a number of reasons. Not being a professional historian, comparing books on the same topic can be difficult since the facts and sources each author uses are mostly the same. Most of the books can be summarized by; a strategy based on politics and greed, the Union invasion blunders into failure and the Feds retreat, Taylor follows but can only pester Banks' with his little army of mostly calvary, and Porter has a heck of a time getting his fleet back to the Mississippi. Unless otherwise noted, most authors take about 200 pages to tell their version from the causes leading to the Red River Campaign to the final outcome. The end notes and bibliographies of these books show most of the authors gathered their information from many of the same sources. A newer book may have more detail because the author's research drilled down a little deeper to shed new light on his version of the story.
Some of the books I have read listed by chronological dates published, starting with oldest:
1879 - Construction and Reconstruction by Richard Taylor - A must read regardless of your views on the CW. If you are interested in what Taylor really thought about Stonewall Jackson or Kirby Smith, this is the book for you.
1963 - William T. Mechling Journal of the Red River Campaign, April 7 to May 10, 1864, edited by Alwyn Barr - A view of the campaign by the AAAG of General Bee's Cavalry Division.
1974 - The CW, A Narrative, Volume III by Shelby Foote - The first 92 pages of Chapt 1, "Another Grand Design" is an overview of both the Red River and Camden Campaigns.
1974 - The Confederate Military Forces in the Trans-Mississippi West, 1861-1865: A Study in Command, by William Geise - A ProQuest dissertation and thesis. As stated in the title, the 315 page thesis focuses mainly on those in command including all areas of the Trans-Mississippi from the Northwest Frontier, Missouri, and each of the Trans-Mississippi states. Mr. Geise offers his views on why Kirby Smith took away Taylor's infantry after the Battle of Pleasant Hill and sent it to Arkansas not always seen in other books. Very interesting.
1992 - Richard Taylor, Soldier Prince of Dixie by T. Michael Parrish - A 501 page biography of the generals life with two chapters covering the Red River Campaign. Highly educated, son of a former president, brother-in-law of Jefferson Davis, and what might be called a jet setter today.
1996 - Admiral David Dixon Porter, The CW years by Chester G. Hearn - This biography provides a good rendition of the river part of the Red River Campaign and Porter's personality. Other than Sherman or Grant, Porter wasn't shy about blaming others if things did not go right.
1998 - War Along the Bayous, The 1864 Red River Campaign in La by William Riley Brooksher - There are a couple of minor errors and more detail in later books. Decent maps.
2001 - Dark and Bloody Ground, The Battle of Mansfield and the Forgotten CW in La by Thomas Ayres - The title was a little misleading. The book starts out in 1860 and more or less follows Taylor's service through the CW. Chapters 15 through 18 are specific to the Red River Campaign.
2004 - One **** Blunder From Beginning to End, The Red River Campaign of 1864 by Gary Joiner - A good read, Mr Joiner's later books add new info. Gary is not only a historian, but a cartographer, therefore he creates many of his maps which provide good detail.
2007 - Little to Eat Thin Mud to Drink, Letters, diaries, and memoirs from the Red River Campaign, 1863-1864, edited by Gary Joiner - The title says it all. I like these types of books because the war is told by those who participated even though it may be through a narrow lens. What they thought and how they felt, sometimes told with humor and their use of phonetic spelling.
2011 - Harvest of Death, The Battle of Jenkins Ferry, Ark, by Joe Walker - The book covers the Arkansas or Camden Campaign which was supposed to work in conjunction with the Red River Campaign to capture Shreveport. Although a book of only 140 pages, it gets into the down and dirty of war. Good maps. A must read in my opinion.
2013 - The Red River Campaign, The Union's Final Attempt to Invade Texas, by Gary Joiner - This book covers both the Red River and Camden Campaigns. A feature of this book are over two dozen short bios of the major players scattered through the book. Each bio is in a sidebar along with a picture of the person. This book also contains reference Appendices for: Orders of Battle for both armies in Louisiana and Arkansas. Vessel name and type in both Porter's fleet & CSA. Timeline of events. Good maps.
2016 - The Red River Campaign and its toll, 69 Bloody Days in Louisiana, March-May 1864, by Henry Robertson - The first four chapters cover the Red River Valley antebellum economics, politics, people, and the effects of war on Louisiana. After that its the same story told by a different author. The end notes seem to indicate less references to the OR's, but more references to previous books by other authors. Decent maps.
Last but by far not least, but too numerous to mention are a number of regimental histories which include the Red River Campaign. These include more information down to the grunts level of the war. Most historians consider the Trans-Mississippi as an insignificant back water part of the War Between the States. Be that as it may, the men who fought were just as courageous, bled just as red, died of the same diseases, and suffered as much as soldiers in any other theater of the war.
(These are only my opinions, so don't anyone start looking for a rope)