The US have been and are still recognized for their military strength.
The US were once recognized for their democracy but this was some time ago. Today the politics - domestic and foreign - of the US is perceived as corrupt and controlled by the economy. Maybe even as stuck in the cold war.
I think this is a fairly typical perception of the US in western Europe, I am quite sure it is here in Germany. Whether this perception is true or false is a different matter. And if you are not living in a well developed country, if you are living in a non-democratic country, you may of course still perceive the US democracy as desirable.
Germany is often looking at Scandinavia because we think they are doing a couple of things in a better way than we do. You would probably have a hard time or have to look quite some time back to find examples were someone suggested we should do it the American way. Even if you forget about politics and look at the economy. Yes, the economy is recognized as really strong, but it is not perceived as superior.
