Take a look here and you'll find:
The FY 2014 Budget requests a total of $8.5 billion for federal
prisons and detention
Note that this only is the federal budget. According to this page, the total expenditure for prisons is 39 billion USD annually.
Over here you'll find that:
The federal government allocated approximately $154 billion on education in fiscal year 2015.
The answer should be pretty definitive because the annual federal budget for education is way higher than the United State's total annual expenditure for prisons.
Conclusion: The US does not spend more on prisons than on public education.