For me...
Target - if I am buying any food or drinks and just for light general shopping. Target is better about keeping food items in stock, they have fresh baked goods, and they carry hummus (which I eat a LOT of). If we want to grab a quick meal, their café is more appealing than the Subway at WM. If I want to pick up a magazine, Target might have something I will actually read, compared to hairstyle, soap opera, and gun mags at WM. Also just a generally more pleasant experience than going to WM and I don't mind paying a little more at Target for lower cost items. Bought some chinos for work here a few years ago because they looked nice and were cheap, but they had plastic zippers that failed within a few months. Sticking to the Haggar outlet from now on, even if it is a bit of a drive.
WalMart - oil or most any automotive purchases, cheap DVDs/BluRays for our cable- and internet-less condo, any electronics purchases over $50 or so. The same TV will probably be $100 less at WM than Target, and I love the giant bins of cheap movies to rummage through.