Similar to the replies above, ME and ID are two distictly different disciplines. Depending on the industry, they complement and rely upon one another - because you're fully engrossed in an ME program, expect to hear that ME is the way to go but it's all about where your passion lies.
As an industrial designer, I worked with lots of MEs, EEs, MBAs, graphic designers, plant engineers, quality engineers, etc and each discipline contributes a specialty. While Mechanical Engineers make stuff work, the Industrial designer sits squarely between Engineering and Marketing and the designer is charged with being aware of and sensititve to both the Engineering package and the goals of Marketing (and Program Management).
I chose ID long ago because the combination of aesthetic, art, science and salesmanship catered to my talents. Find your passion and your career will follow.