The biggest difference between the roles of the two sections was, of course, the fact that the North was generally running the Reconstruction governments while the South was in a subordinate position. While the Reconstruction governments were made up largely of Southerners, the North had power over those governments and was therefore the dominant party.
The similarity in their roles became more apparent as enthusiasm for Reconstruction waned. A group of "liberal Republicans" (see this link) came to agree with the South that the Reconstruction governments should be done away with. They believed that these governments were corrupt and the African Americans were not ready to govern themselves. These liberal Republicans, along with Southern "redeemer" helped to end Reconstruction.
At the beginning of Reconstruction, there was more of a difference between the roles of the two sides. As time went by, the differences faded and eventually both sides played a part in ending Reconstruction.