Many historians have argued that the Civil War resulted in a stronger national government as Lincoln centralized a great deal of power in the Federal Government as a means to better fight the war. Gary Gallagher and Joan Waugh in their 2015 book The American War: A History of the Civil War Era argue that the Confederacy more than matched the Union's centralization of power. To put it basically, the Confederacy found that it's easier to fight a war when you have a strong federal government. In 1862, the Confederacy implemented the first national draft in U.S. history. Some individual union states had used drafts to fulfill quotas, but the Confederate draft of April 1862 was the first national draft. Gallagher and Waugh note that it was a response to the pending loss of the original volunteer forces, who had volunteered for a 12 month period. The draft would later be expanded to apply to men between 17 and 50 in age by early 1864. There was a lot of criticism about an intrusive federal government, but what proved really controversial was the provision that allowed a draftee could hire a substitute. This led to the belief that the poor were fighting the rich's war.

War is expensive, so the Confederacy used taxes, loans, and primarily paper money to fund the war, all signs of a more centralized national government. An impressment act allowed the War Department to take food, livestock, and slaves from citizens to benefit the war. Although this wasn't implemented until March 26, 1863, it was only formalizing something that had been happening since the beginning of the war.

Naturally, there was criticism of the overreaching federal government depriving the states of their rights. Joseph E. Brown, the governor of Georgia, was a public opponent of conscription. On the other side, General Lee argued that winning the war was the most important issue at hand and everything must be done to accomplish that. Regardless, there was desertion and harsh opposition to Richmond becoming more and more centralized.

To answer your question, the Confederacy began to centralize a great deal as a means of better fighting the war. I'm hesitant to say that it was as centralized as the Union, only because the Union's centralization continued after the war to a certain extent in the reconstruction of the entire nation. One book that talks about that is Heather Cox Richardson's West From Appomattox: The Reconstruction of America after the Civil War which argues that Reconstruction began in 1865 and ended when Theodore Roosevelt was president.