This is a question that I am struggling with too. I like all intellectual, mind driving things, so mathematics, science, robotics, and engineering fit the bill perfectly. But one needs to be more specific than that when choosing a career. Here is what I have thought of as my options:
-Mechanical Engineer
-Electrical Engineer
-Computer Scientist (programmer, I guess)
-Applied Mathematician
-someone who works in Mechatronics (basically robotics, ME and EE combined)
Currently I am leaning mostly towards a mechanical engineer.
I really enjoy logical, intellectual things, like I said before, and I thrive in the logic of programming, so I am in that group on my team (also because I'm sure I have some level of OCD and I drive the other programmers nuts by cleaning up our code
). However, I think personally something like applied mathematics or programming would be too much logistics and not applied and hands on enough for me as a job. That is why I am leaning on mechanical engineering. However, I have again wavered because ME might not have enough logic enough for me. So those are my thoughts on my situation.
Please understand that I am talking about the extremes in these fields. Like was said before, they are very gray and you end up doing very similar things in each. Depending on where you work and what your specific job is, you also may be doing many different types of tasks and projects. And of course people who have these jobs feel passionate about them and the aspects I mentioned above. They are not what make or break a career. But those extremes help define what differs between these careers, which is the point in choosing between them. I don't want to end up saying "I like my job because it's intellectual, but I wish I had taken up ... because I would have liked more of ... "
So, like me, I suggest that you keep researching to see which one has the best aspects for you. Joining FIRST is a great way to do so. Posting here is also a great idea. Ask the college(s) you are planning for. "Job shadow" someone. I personally can't give too much knowledge or experience because I am deciding myself and haven't worked in one of these jobs, but I hope that gives you some ideas.
gblake made a good point. Unfortunately, not everyone can pay for 2 degrees or have the time to learn each. There is a lot more to learn, know, and remember by doing so. And it might be better if you can focus your efforts and passions towards one area. If that sounds like it would work for you, go for it! I would be very excited if I were to do so, you know, the more the merrier. But personally I would not for the above reasons.
Hope that helps!