Answer:
The New South emerged from the Old one, after the Civil War ended, and through the Reconstruction Era. The differences, and similarities between the two were many, as we shall see.
First, let´s go with the similarities. The South has always been different from the North because of its richness in natural resources, and especially agricultural products. It is this reason that made the South so unique with its big farms, its plantations, and its big production of tobacco, cotton, and other such primary agricultural products. As such, the Old South depended on one thing: hands to work the land. And these hands came from slave labor. After the Civil War, slavery was abolished, and therefore these Southern plantations lost their laborers. However, it is now known that first, the New South re-employed a lot of the slaves that had been freed, and many retained their old slaves, even if now they were given pay for their work. This did not change between the Old and the New South. Another similarity between them two is that the dependency on agricultural products did not change after Reconstruction.
On the differences, these emerged too. First, the actual change from using slave labor, to paid labor, even if the workers were African Americans and they were not treated much better than before. Second, with the initiation of industrialization, especially in the North, a lot of producers and plantation owners in the New South became interested in acquiring these new technologies, and thus helped with the industrialization of the South. Also, manufacturing, which had originated in the North, and for which the South had been slow to become interested in, started to grow and develop, particulary in some regions of the New South.
These are only a few of the ways in which the economy of the New South was different, and similar to the economy of the Old South.