MD’s problem is the county tax. Without that, the taxes could be a wash with NH depending, of course, on income and house price. NH’s property tax rates are out of control. 2%+ in many areas.
When people talk about moving for tax reasons, in most cases what they really are doing is moving for quality of life (weather) or bang for your buck (cheaper housing) reasons. The taxes just don’t make that much of a financial difference in the vast majority of cases.