A major difference that no-one in the thread has yet raised is that in Europe flight within Terminal Airspaces (TMA) of major airports is mandatory IFR. In the US airports usually run VFR, when the airspace becomes IMC and traffic is required to fly IFR the capacity of the US airports reduces sometimes significantly.
The practice of clearing an aircraft to land well before it can be guaranteed that the runway is clear for that aircraft to make a landing is not easy to accept by those who would normally only provide a formal landing clearance when the runway is allocated solely to the landing aircraft. Providing a clearance to land earlier is passing a controller's responsibility to the pilot. Yes the clearance can be withdrawn, but only if communications do not fail. So provision of early landing clearance before the runway is actually clear, puts the system into a fail dangerous rather than a fail safe state. In the US this is accepted, as is allowing passenger aircraft to land without a clearance as happened with the famous DCA sleeping controller.
This is just 'a difference' in approach (pun intended). It works, like all things, until it doesn't.