Europe wan'ts an own system because the next step will be to create a real european army, wich will use their own satelite system.. USA has proven in the past to shut down the gps directly in certain areas when in conflict and the Americans don't give a sh*t that everybody relies on their (military at first) GPS system
The American's has also done everything that's in their power to stop the Gallileo project, but hey 'space' is for everybody and without doubt chinese people will put their own system in space as soon as we western people have trained enough chinese engineers...(thats the problem with googs we train in our universities, they actually go back to china after graduating...not like the africans :-)