To take one of the most extreme cases, the Town of Rehoboth Beach last did a property assessment for tax purposes in 1968 so homes in the town are still being taxed at 1968 assessed value.
A home that I purchased in 1976 while living in Rehoboth cost me $29,500.00 that self same home (no longer owned by me, unfortunately, I sold in 1979) I sold for a client last year for a little under $900,000.00. But because taxes are assessed on the last assessed value of the property which was 1968 that is the tax that the new buyer pays on his $900,000.00 purchase.
To give you another example, I sold my step-daughter a home last week for $189,500.00, a 3BR, 2BA Ranch style home, less than 10 years old on 3/4 of an acre lot and her taxes on that purchase because of the last time that property value was assessed in her area amount to just $561.00 per year. So if you pick wisely where you buy your home in Delaware, property taxes are so insignificant as to be not even part of your financial equation, when buying your home.