I don't really know if there is an advantage or not (I'm not an engineer), but since you're only JUST starting out in university, my primary suggestion would be for you to wait to make the decision until your feet are wet in the program. You might stick with engineering, but find out that one of the other specialties interests you more than being an ME, or you might find out that engineering isn't what you expected and switch to another major entirely. I don't know very many people who got masters degrees in engineering except for those who needed more time to find jobs after graduation. I would think if you're interested in an advanced degree, it would be a PhD you'd be after if you wanted to teach the subject...and then you might opt for a masters as a stepping stone in that direction. Some of the engineers here might have better insight on that though.
Nonetheless, my emphasis is that you should get through a year or two of university before you start worrying about grad school vs heading straight to work. A LOT of people change their minds about majors between high school and sophomore year at a university.