When was the last time any of us calculated a solution to partial differential equation? Drew a free body diagram? Calculated a stress-strain relationship? Oh, it was in school? Since you graduated, have you done any of the things you learned how to do in school?
An Engineering degree is an indication that you are capable of learning some truly esoteric things, but mostly it is an indication that you have the ability to approach problems logically.
An MBA is an indication that you can master the range of skills that are required to run a business.
These two skill sets are not mutually exclusive. An MBA that cannot approach problems logically will always make a lousy line (or engineering) manager. An engineer who is unable to run an economic model or evaluate a supply chain or treat people as humans instead of cogs will always be a lousy line (or engineering) manager.
Someone who has demonstrated both sets of skills has a really good chance of success in management even if they lack formal credentials in either area. I've worked for MBA's that were effective managers. I've worked for engineers that were effective managers. I've worked for people without either credential who were effective managers. The conversed of all of those statements is also very true--I've seen MBA's, engineers, and "others" who were horrible at managing people, projects, and companies.
A degree is just an indicator of a persons ability to show some level of mastery of a specific list of esoteric subjects. Beyond that, it is just a piece of paper.
David