The Programmer's SE, as its FAQ says, is "for expert programmers who are interested in conceptual questions on software development."
Stack Overflow accomplishes a different, needed function -- troubleshooting source code, algorithms, and tools (SO FAQ). As others have noted, a high Stack Overflow reputation may or may not aid in getting a good job. Joel Spolsky certainly thinks so, but others disagree. I would say that even the highest rated Stack Overflow questions tend to have somewhat rote answers. They are relatively easy to rattle off one's memory, if you know the answer, or look up in a book. For most problems of that sort, there is a simple technological reason, easily communicated, why it is thus.
In the real world, programming occurs on a team of people for whom it is most of the time hard to escape being subjective. Some of the questions are managerial, but many are not. Adopting "new" methodologies, like automated unit testing and code reviews can be hard. Having a CS degree but not feeling like you know how to program is a real issue. Rising above the subjective nature of these questions and providing useful guidance is a challenge.
Communication is a vital aspect that sets apart intelligent life forms from unintelligent life forms. Communicating persuasively and objectively in the presence of subjectivity and strongly held opinions is a test of intelligence (and also humility and tact) that is useful to an employer.
Borrowing from the title of Joel Spolsky's helpful book, Smart and Gets Things Done, perhaps Programmer's SE measures the Smart and Stack Overflow measures the and Gets Things Done.
