In the US, your funding primarily comes from your PI. You may have to supplement it via TAing some semesters depending on your group's resources. Even if you are lucky enough to get something like an NSF GRFP, that wont fund your full five or more years as a student.
Duration is another difference, 5 year PhDs are rare in Europe.
The Netherlands mostly has 4 year programs, Germany mostly seems to have 3 years.
At the same time, PhDs here require a MSc (2 years usually), which in turn requires a BSc (3 years usually). So in the end, total time from start to PhD doesn't differ too much.
