Theoretically with an LVT, if the value of the property goes up because you restore and extend it or convert it into a dozen flats the tax stays the same (but still increases if the value increases because youre lucky enough get a good school and a light rail station in the area as the result of others' actions). In practice, it's somewhat difficult to separate the two which is why property taxes are more common (also because the multistorey apartment block built on similarly valued land to the house next door has a lot more people with the ability to pay and the expectation of having local services paid for)

The other difference is that proponents of LVT often argue it should replace other taxes like income tax. But regardless of theoretical efficiency criteria, it's a lot easier to persuade people that a large fixed portion of their earnings are the government's share than give them an enormous bill for the valuable land their house sits on and tell them if they're not earning enough to afford it they can always move (as long as they can find a buyer...). Which is why LVT has been 'inevitable' since before the Industrial Revolution without it being very widely experimented with