Career choice questions are never going to work on Stack Exchange because they're too specific to the poster. Programmers offers this great diagram:
“Should I study this or that” falls under the “just you” category. Very few career-related questions fall into the “all programmers” category. Furthermore, on this site, I don't think there's any analog of “all programmers”: this is a site about computer science, not about computer scientist.
“How do computer science and software engineering relate and differ?” goes in the right step of generalizing over individual issues. But I fear that it's far too broad, and it isn't directly applicable to education and career choices anyway.
Every university will have its own breakdown between fields. Computer science may be bunched with mathematics or with software engineering or with electical engineering. It may be a matter of core courses or electives. There's no general rule as to what course belongs or doesn't belong in which program.
Furthermore, your educational background doesn't lock you into a career path. Just to give an example, at my job (embedded software development), we have people with PhD's, people with an electrical engineering degree and people with a CS/programming degree. We're all doing broadly the same job. Sure, we tend to ask the PhD's when there's an architecture to design, and the EE guys when there's soldering to do. But that's determined by competence rather than by asking people what degree they have.
The difference between CS and SE is a broad topic, and the answer wouldn't be useful for career choices. I also foresee turf debates. (Try dropping it on Meta Stack Overflow and you'll get a popular response that software engineering is what's useful and CS is “useless theoretical wankery”.) I don't see what this reference question could achieve.