Arguably, Jefferson Davis exercised as much "big gubmint centralized control" over the Confederacy as Lincoln did over the Union.
Actually the anecdotal evidence is to the contrary though during a war a President will tend to act autocratic in many ways.
I have read a letter from Joseph Brown, the governor of GA, complaining to Pres. Davis on the unfairness of how soldiers from each state was provisioned. GA was not getting any supplies from their sea port( Savannah was completely shut off) where at the same time both AL and NC had fairly open sea ports for most of the war. Soldiers from AL and NC stood out on the battle field because they looked well shod and had good uniform where most of the rest of the Army looked like scare crows. Gov. Brown thought AL and NC should "share the wealth". Pres. Davis responded that there was nothing he could do about it and that the governors would have to work that out for themselves.
I find this type of info very telling.