There's no comparison.
Georgia's Governor Joseph Brown was a Confederate patriot, who championed secession and acts of force which led to war.
During the war, Brown did everything possible to keep Georgia troops and civilians supplied with necessities.
Brown's problem was two-fold:
But Brown did not publicly oppose the Confederacy, or the war -- just the opposite.
Instead, he lawfully worked hard -- with increasing backing from Georgia's legislature -- to support and defend Georgians, over the demands of the Confederacy's central government.
So there is no comparison between Georgia's Governor Joseph Brown and Ohio's former Congressmen Clement Vallandigham.
Sorry, Brown did finally oppose the war:
Yes, after the war was obviously lost, and the Confederacy itself had no power to discipline Brown.
From my above link on Brown:
the hallmark of his wartime administration was his resistance to the authority of the central Confederate government, a policy that was soon copied by some other Confederate governors and that helped to undermine the overall war effort. Governor Brown's opposition surfaced in many fields. He opposed the army's impressments of goods and especially slave laborers. He frustrated Confederate efforts to seize the Western and Atlantic Railroad and to impose occasional martial law. He bitterly criticized Confederate tax and blockade-running policies.
Brown was more effective against the Confederacy's war effort than Vallandigham was against the Union war effort.
I have to be away from the threads for a while. We are going to have 50 guests in our house in a little while. Ciao.