Wal-Mart has more social responsibility than Target actually, believe it or not. Target has an amazingly good image for a company that has an absolutely atrocious history.
Target is simply better that engineering their image than Wal-Mart. Wal-Mart treats their employees better than Target (which isn't saying much), and they engage in much more beneficial community sponsorship projects.
That said, Wal-Mart is *not* a socially responsible company. But everything is relative, and they're much better than Target.
Now if you want to shop socially responsible, shop Costco...