I am not that familiar with NE LACS, but here are the expected incomes from various public and private schools in Wisconsin. All information is via The Economist:
http://www.economist.com/blogs/graphicdetail/2015/10/value-university
The two big research universities in the state are UW Madison and Marquette, and their salary outcomes are as follows:
UW-Madison:$51,000
Marquette: $55,600
So in this case, the private school has a small but significant income advantage over the comparable public school. Lets looks at the smaller private LACs versus the directional public colleges in Wisconsin:
Lawrence - $42,800
Beloit - $37,900
Ripon - $42,800
Carthage - $42,400
Concordia WI - $40,700
UW-Stout - $42,000
UW-Steven Point - $39,400
UW-Eau Claire -$43,400
UW-LaCrosse - $44,100
UW-Whitewater - $41,200
UW-Green Bay - $39,600
UW-Oshkosh - $40,500
UW-River Falls - $39,700
UW-Milwaukee - $42,000
There is very little difference between the two sets in terms of expected income outcomes. However, Lawrence charges $44,844 in tuition, Beloit charges $45,050, Ripon charges $36,514, and Carthage charges $38,375. Tuition at a non-Madison UW system school is under $9,000 for in-state residents, with OOS charges of less than $17,000.
Like NoVaDad99 said, attending a private school versus a public frequently is just about bragging rights.