Thanks for good info.
The issue I have with live view on moving subjects is that they move. Live view manual focus does take some time. Other than that I consider LV focus to be the best method.
Actually a tripod will help focus in moving situations too, both manual and auto focus.
Even when shooting a moving model using a video tripod with a fluid head will help
auto focus by reducing jitter. By reducing jitter the AF system gets a cleaner image to work with.
IS lenses when working hand held also help the AF system in a camera.