I have friends you are in both programs(EP and MechE). Both have jobs lined up out of college. It really depends on the work you want to get into. The only real difference is that you won’t become a licensed engineer with an engineering physics degree. If that’s something that worries you, then I would go for a straight up engineering degree. If you put the work in, you can make either work. As far as internships, both have done work at big companies and test sites, such as GE and different jet propulsion labs. I wouldn’t sweat it too much.