I haven't looked into the CPS high schools (my oldest kid is 8!) but isn't Whitney Young a selective enrollment school you have to test to get into? Assuming your son has been accepted, congrats!
Here's the CPS pages for each
Whitney M Young Magnet High School --
http://www.cps.edu/Schools/Pages/school.aspx?id=609755
Lincoln Park High School --
http://www.cps.edu/Schools/Pages/school.aspx?id=609738
Both school are diverse.
In the Scorecard section, Whitney Young looks to be higher in everything? Sometimes significantly so... For instance, in the "Meet/Exceed PSAE State standards" Lincoln Park is very good with 67% compared to the CPS average of 31.5%. But Whitney Young is 96%!
Of course there are other factors to consider such as how convenient it is for your kid to get to school each day (e.g. a 1.5 hour bus ride or 5 min walk), but all else being equal I would go with Whitney Young.