Everyone has covered the owner occ/versus primary residence piece and the county by county millage difference.
However the other side of the coin must also be considered in order to evaluate. You will find that NC has a much higher tax rate than the SC owner/occ rate, but typically a tad lower than the NOO rate (again this will depend on county).
Where the calculation gets even more tricky is the value premium placed on a home by location.
If you are looking at Charlotte for example, the national builders who operate in both markets will charge a premium on Ft Mill and Lake Wylie areas over Charlotte addresses for the same floor plan, because they know owner occ buyers will pay the premium because their monthly payment will be the same for both neighborhoods.
If you are in Rock Hill here is a fun Saturday. Pick a builder. When I did this experiment I used M/I homes...for no reason other than I knew where each was. I went to a Sutton Creek (RH SC) model home and then to one in The Blume (CHT NC)...looked at the same floorplan. Had the sales rep on duty run me numbers based off the same criteria and the exact same layout. The NC home sold for a lower price point but the PITI was within $5 because these larger builders are now selling off payment just like a car dealer.
Those value numbers will skew the conversation as well.