I'm too lazy to do anything but a cursory search, but it looks like it breaks down like this for higher education spending, according to a 2015 report:
Federal: $75.6 billion
State: $72.7 billion
Local: $9.2 billion
Although the funding between State and Federal are similar, the way those funds are spent may be different:
"The federal government mostly provides financial assistance to individual students and funds specific research projects, while states typically fund the general operations of public institutions, with smaller amounts appropriated for research and financial aid."
