I am surprised DL is that much more than NK. I am flying DTW/MDW for the holiday this weekend, and priced southwest as well, and for that short of a route WN was over $150 more, so even if the kettles had to pay the $25 each way to check a bag they are better off on DL than WN. Last couple trips that I have booked on DL when I knew WN flew the same route, I have checked WN's site as well out of curousity, and DL is always cheaper and Direct.
Make sure to allow extra time than you normally do out of DTW if you are on NK. Last couple times I have taken WN the lines at the north terminal have been long.