| Well, I can't comment on the level of "respect" that different majors receive but it is tradition that EE/ChemE/ME degrees are much more versatile and usually are heavily recruited.
I think you need to evaluate why you are doing your Bioengineering degree and what exactly you want out of it. Don't do the degree simply because it is ranked high at your program--rankings don't really mean much and if you don't have any passion or interest in your major, you'll suffer.
Next, Bioengineering is a pretty specialized degree. While ME/EE/ChemEs can obtain BME jobs after graduation or with a year or two of supplemental studies, a BME won't be able to get the ME/EE/ChemE jobs. So, getting a non biological/medical job might be difficult--you probably won't be hired as a field engineer or pipe engineer. As for business, most of those recruiters tend to recruit engineers regardless of their degrees, just because of our analytical skills. It won't be harder with a BME degree but you'll have to actively seek those positions, which are usually for analysts/consultants.
BME would be perfect for Biotechnology jobs.
Finally, if you have an interest/passion for the degree--its not useless at all. Yet, if you want a job in something that doesn't relate to biotech/medical, a BE degree might not be your best option. | 
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