Constitutionality of Zoning (From a Plan-link posting and reply ["ZBA Question"], February 2011)
Relative to property rights, the NH Constitution generally provides a greater degree of protection than the US Constitution’s 5th Amendment (see, e.g., Community Resources for Justice v. Manchester , 154 N.H. 748 (2007)) and so the NH courts will typically review such cases with reference to the NH Constitution (but that also depends on how the parties frame their cases). In other circumstances, the US Constitution may provide greater protections (I have no examples off-hand); as the "supreme law of the land", the US Constitution may be the deciding factor in cases, other laws notwithstanding (including state constitutions).
Recognize also that both the US and NH Supreme Courts have held that under the US and NH constitutions, respectively, zoning is a legitimate exercise of the government’s police power. See, e.g., Euclid v. Ambler Realty Co., 272 U.S. 365 (1926) and Sundeen v. Rogers, 83 N.H. 253 (1928).