10 years ago, I would have agreed that enginering was the way to go. Today, I would probably discourage it.
Why? Are there tougher classes than Engineering courses in college? A few, but Engineering courses are HARD. Physics, Comp Sci, Programming, Math, Chemistry, Quantum Mechanics, ect. And when you have this degree, you can be laid off at a moments notice.
However, if you have a business degree - and you make the grades - you can be the schmuch that blows the company's earnings, causes the layoffs, and still be the guy watching the engineers drag themselves across the parking lot from your desk. Your job will be secure.
Anymore, I'd think seriously about jobs that by definition, can not be exported. Medical comes to mind.
Sure, I get paid well; I've got the experience and the skills to make a good salary. But, if some schmuch decides that we need to cut the technical talent to generate better quarterly revenue projections - I'm kicked out the door right away. Managers almost NEVER get laid off; and all a manager needs is a business degree. Very few Engineering Managers have any technical skills whatsoever.
Then become a manager or quit your whining!