But to be clear, if you're not already a showing talent as a programmer, and you want to be skilled as one, if you have to pick between mathematics and CS, pick mathematics and learn a programming language on the side (give yourself a challenging, sizable project which you care about - and get it done, even if it takes a year or two). The cognitive skills you will learn in mathematics will do more to cover for your gaps as a programmer than most CS programs will teach you.

Bear in mind, I'm talking about effectiveness, rather than credentials. Credentials are an entirely different matter - and like most status games it is a constantly evolving mess.