One massive difference: Property taxes are state and local taxes, which are not barred by the Constitution in the way that federal property/wealth taxes very likely are (absent an amendment, of course).

(There is debate on this point; I personally find the side arguing that such a tax would not be barred as needing to use fairly tortured lines of reasoning to arrive at their conclusion.) If you can’t pass a wealth tax federally, then whatever state wanted to compete on having a low/zero wealth tax would find plenty of wealthy takers as residents.