Germany has 104 universities. The German system is peculiar in being very egalitarian. In principle, all universities are equal. There are differences, of course. Internationally, the old universities such as Heidelberg are the ones that are more recognized. But there is no layer of élite institutions in the US, UK or French fashion, which would apply stricter entry criteria or be noticeably financially better off. This is the fruit of the immediate post-war policy of the German government, which sought to provide for equal development of all German regions.
US education generally enjoys very high reputation around the world. In addition, many Americans want to be able to spend a semester abroad but still be able to transfer their credits back home.