I'm not in either state you mention, nor am I a lawyer, so I cannot give legal advise, but I am a Tax Assessor for the county in Georgia in which I live.
So far as property taxes go, the state/county where it is based is most likely to claim it for themselves. In Georgia the property taxes are paid to the county where the aircraft (or boat) is prinicipally based. The law in Georgia defines "principally based" using a minimum number of days per year (which I don't recall off hand).
Sales taxes are an issue that varies greatly with states. Again, from experience of myself and others in GEORGIA, if you bought from a dealer either in state or out of state, you will owe Georgia the sales tax. If you paid 4% in Louisiana when you bought from a dealer (like a friend with a 180 Cessna did) and brought it to Georgia (where the county where his address he registered it to gets a total of 7% [4% state + 3% local option]) he had to pay the difference from what he paid in Louisana.
If it was a private sale, no dealer involved, either from in or out of state, there would not be any sales tax in Georgia, this has been through the courts in Georgia.
You need to call the state department of revenue for both SC and NC and get the scoop from them, check their web site, get it in writing if you can, so when the local tax officials come looking for money, you can show them the real deal, what the state boys say.
A lawyer friend told me he had tried everything to dodge property taxes for his expensive twin based in Georgia, he said he finally found one thing that worked, he registered the airplane to a Delaware corporation which he created, and then moved the airplane out of state in late December and brought it back in state in early January and had unrefutable proof of where the airplane was during that time. That was alot of work to get out of paying taxes.
Charles