I'm not sure it really matters what your college degree is as long as it is in the right ballpark. Something to consider is that there is a small pool of "really awesome" jobs. For example, thousands if not tens of thousands of students take orbital mechanics every year, but there are almost certainly less than 1,000 people that do orbital mechanics as a full time job. I think that most engineering jobs are actually pretty cool, but if you walk into an engineering degree absolutely set on a specific position, chances are fairly good you'll be disappointed. I didn't even know my job existed when I started my freshman year of college!
My standard advice is do Formula SAE, Formula Hybrid, AeroDesign, DBF, Concrete Canoe, Steel Bridge, etc. They are a much better approximation of the real world than your classes are, and they give you a ton to talk about in interviews. Even more importantly than giving you something to
STAR about, you actually learn a lot about engineering and people. But you've done FIRST, so you probably knew that.
I learned way more in my 3 month internship than I did in my first two years of college, and I've spent most of my last year waiting to start working. However, I can safely say all of those 3 months would've been totally lost on me if it wasn't for those two years of groundwork.