Ok, even though they are both "department" stores they offer different merchandise. Target offers everything from soup to Bridal Gowns [see Isaac Mizrahi] where Kohl's sells things for the home & clothing [shoes & accessories].
Personally, when I want clothes I go to Kohl's. Though Target offers Isaac, their Go International line & such the offerings are not a good match for me - whether it be in fit or quality. Kohl's offers it's own line lines like Target including some designer lines - Daisy Fuentes, Adidas, Nike, Columbia, Chaps & if when I read is true - Vera Wang will be designing a line for Kohl's as well.
Just my take on things!