I can offer some insight for you because I have a CS degree and a MBA. What follows may sound like I'm trashing Computer Science, but that is not the case at all. CS is a good engineering degree but your goal is to be CIO or CTO, not an engineering manager. Computer Science is 100% hard-core technical. Algorithm analysis, theory of programming languages, design of operating systems, automata theory, network theory, database design. It is an engineering degree. Interesting stuff but not really useful in the real world. It is not a well-rounded curriculum. It is good training for a R&D engineering job that is heavy into software or systems design and development. You won't get any exposure to the business side of things and won't learn important soft skills, either at school or at work. (Soft skills include working in teams, subjective out-of-the-box thinking, making presentations, writing). Engineers with no knowledge of business usually make lousy C-level executives. It's a big jump from computer science into a CIO position without some knowledge of business strategy and finance to go along with your technical knowledge. It's a smaller jump to a CTO position but far more companies have a CIO than a CTO. (All companies have a CEO and CFO. I estimate about 75% have a CIO. In some cases, the CFO actually doubles up as a pseudo-CIO. I estimate less than 50% of companies have a CTO). A BBA will give you only very limited exposure to technology. But it is still a smaller jump into a CIO position from a pure BBA than a CS degree. The technology knowledge related to business processes that a CIO would need to know is not extremely difficult to learn. I think there's a lower ceiling with a CS degree. If you want to stay purely technical, a CS degree is great. If you want to move beyond mid-level management, you'll almost certainly need some knowledge of how businesses operate.
I've made the same recommendation every time I answer a question like this on TR. And this type of question gets asked a lot. If I were starting all over, I'd probably go for a BS in MIS/CIS, work for about five years, then do a MBA. The MIS/CIS will give you exposure to a wider variety of [u]practical[/u] technical skills and you'll also learn some accounting and finance. With a MIS degree, your first job will more likely be working with business systems and applications and you'll make a lot more connections a lot more quickly with people in business management (as opposed to technical management like you would from a CS job).