FIRST wasn't around back then, but I decided in High School, back in the '60's, that I wanted to be an engineer. So I did. Went to Clarkson, as a matter of fact, BSEE 1970. It was a good thing.
Now, 33 years later, it's still a good thing. Although I picked up a couple of MBAs in the '80's, I still consider myself as primarily an engineer, and really enjoy working with FIRST. Science and technology is mostly FUN. And the math isn't really that bad (I can say that now, but please don't ask me to solve a partial differential problem right away, without some brushing up.)
If you think designing the robots is as much fun as building them, go for engineering.
Regards,
Bruce C.