The two are right next to each other, both along A1A directly on Ormond Beach.
Royal Floridian was built sometime between 1965-1975 and was originally known as the Pagoda Inn, then the Granada Inn and eventually was transformed into the Royal Floridian as a timeshare resort. Royal Floridian South was built specifically to be a timeshare, thus the units are much more like condos than RF.
Comparing the two resorts, RF South units have granite countertops, larger/nicer kitchens and stackable washer/dryers. The RF units (even the larger 2-bedroom and lockout units) have smaller kitchens, less expensive finishes and no washer/dryers.
Clearly the units at RF South are nicer; however, RF has a few advantages of its own: the pools (indoor and outdoor) are both at the RF, thus are more convenient to those staying in the main building, (almost) all of the units are oceanfront (at RF South only about 1/4 to 1/3 of the units are oceanfront) and the other amenities (bar, shuffleboard, etc.) are in the main building.
Neither place is bad. All depends on what is important to you.