Although I would point out the US system is pretty efficient, unlike our health care. We spend the most there too.

In terms of expenditure for higher education alone (i.e. including but not limited to research) the EU has an expenditure of 1.1% GDP, while the US is 2.3% GDP.

From the EU2020 site:

"American universities have far more substantial means than European universities on average, two to five times higher spending per student. The resources brought by students themselves, including by the many foreign students, partly explain this gap. But American universities benefit both from a high level of public funding, including through research and defence credits, and from substantial private funding, particularly for fundamental research, provided by the business sector and philanthropic foundations. The big private research universities also often have considerable wealth, built up over time through private donations, particularly from graduate associations.

The growing under-funding of European universities jeopardises their capacity to attract and keep the best talent, and to strengthen the excellence of their research and teaching activities(1). Given that it is highly unlikely that additional public funding can alone make up the widening shortfall, new ways have to be found of increasing and diversifying universities' income. The Commission plans to conduct a study on the funding of European universities in order to examine the main trends in this area and identify examples of best practice."