Practical experience (of a practicing engineer) shows that the value of an engineering degree outweighs that of one's work only in the first couple of months, or even weeks, on a job. The skills of incompetent engineers are in significantly less demand than that of incompetent managers (sadly). Unlike an MBA, the engineering diploma isn't worth the paper it's written on the moment people realize you're clueless. It's not a very good safety net :-).
Out of the top-20 MBA programs, STEM undergraduate degrees are about as common as business/economics undergraduate degrees: http://www.beatthegmat.com/mba/2009/11/20/which-undergrad-ma....
For a business major to do the vice versa would be virtually impossible (programmer is possible, but not 'engineer' in the traditional sense).
I am pretty sure I could teach just about anyone who is motivated and interested enough math/chemistry/physics/computer science to get through any given engineering degree in those areas.
I think the amount of business people who are motivated to and interested in learning the engineering skills is way lower than the amount of engineering people who are motivated to and interested in learning business skills, but that isnt about ability, that is about motivation and interest.
Engineering interest maps much more directly to engineering education than business interest maps to business education.
You don't see to many people doing that switch, but I'd attribute it to factors other than any kind of ability chasm. What we do isn't rocket science[1].
[1] Unless you are a Kerbal Space Program developer. Then it is rocket science. Of the fun kind.
I took a single class at the USC Law School on Constitutional Law. It was considered a brutal general education class, but myself and some fellow engineers in the class found it absolutely trivial. Turns out case law has many similarities to formal logic.
An engineering education gives you a huge toolset with which to model and solve different kinds of problems, a toolset that non-engineers simply do not possess.