my suggestion: major in one, and minor in the other. your course schedule should not be so full that you cannot take some courses just because you WANT to.
no matter which career path you choose, there are some math courses you will want to take, regardless:
Combinatorics (discrete math)
Numerical methods (a very handy "bag of tricks" for solving "hard problems")
Linear Algebra (you WILL handle data arrays. yes. you will.)
Mathematical Logic (insight into binary structures, and clearer thinking all in one course!)
some of these classes will have pre-requisites, so there will be "others" you need to go through to get to these. the good news is, the pre-requisites are also likely to be required for either major.
my advice is to study what you like the most. when you near the end of your life, how successful your career has been may not mean as much to you as how much you enjoyed the life you chose. choose wisely. and remember: whatever you DON'T learn in college, you still have the rest of your life to learn it AFTER. life isn't "either/or" it's "first, then next".