Depends how the property tax is calculated. In some states, tax on new built property (condo, SFH, etc) is dertermined by the sales price * a tax ratio. The old property is taxed based on old, old price, which is used as tax asessment base. The town may not reassess the amount for years, so the tax is very low comparing to the recent built property.
但是你买了房子, 不管新旧 都会按你买入价重新评估 This is not true. Again, depends on the state and township, tax may not be reassessed after each sales transaction. Unless the house is rebuilt, then the town will reassess the tax.