Just my two cents: Thinking about how hospitals market themselves, at least in English, "most important" sounds a little bit unusual to me.
The hospital usually wants to be thought of as the best, the most outstanding, the top trauma facility in a certain area. To me, "leading" is just a slightly more professional way of saying "We're the best!" Best in what way? We don't know. This kind of marketing often leaves out the fine details. But I just get the sense that they aren't trying to say "We're the most important!"