Do both if you can. CS is everything about how computers and software works. It is the hardcore hands on stuff (and the most fun). SE is about the development process - defining requirements, writing specifications, testing, etc.
Although CS is more fun and I find more exciting, SE gets you the furthest up the food chain because it leads to the design and leadership roles.
Unfortunately, being a programmer is bit of a dead-end position in the commerical world. Many companies treat you like trained monkeys that can be shipped in and out. Look at the way programming roles are outsourced to India. Architects and team leaders are at least a little more valuable. Project managers are better still. And if you can sell something, even though it seems like an immoral and unworthy skill, salesmen seem to rule the world.