I graduated as an engineer and eventually became a business analyst/consultant. If I were in your position I would choose the business degree and either a minor in software engineering (it's not the same as CS) or learn SE using web resources/courses.

Since you're not in SV and I assume in some other IT dominated locale, you are likely to earn far more in the business world with strong IT skills. Business knowledge and experience opens doors to many industries so you can gravitate to areas that appeal to you. As a software developer your domain specific experience will be far more critical than your knowledge of selection of software tools and frameworks. But jobs for software developers are mostly defined by your technical experience and thus difficult to transition between domains.