The Project on Student Debt gives information in average student debt at graduation for both public and private colleges.
http://ticas.org/posd/state-state-data-2015#
From what I can tell the more highly ranked liberal arts colleges tend to leave graduates with less debt than the state flagship while less competitive LACs leave their graduates with more than the state flagship.
For instance, among Vermont colleges in 2015 the average debt for a University of Vermont graduate was $27, 276, whereas the average Middlebury (USNWR #4) borrower owed only $17, 975 but the average Marlboro College (#128) kid left school in debt to the tune of $29,478.