I've got friends in both fields.
CIS Seems to be more oriented towards the management end of computer systems. For instance you could become a leader of an ITS team or the manager of an IT dept.
Computer Science is a degree that will get you into a programming position. You'll learn many computer languages like Java, C, C++, SQL, VB and many more. You'll probably learn some of these in your CIS degree too.
As far as the class requirements, more than likely your first 3 years in both degrees will be very similar. Get your prerequisites out of the way along with some light programming courses. Then you'll begin to split as the CIS degree goes into management classes and applied computing while the BS in CS goes into advanced programming like computing theory and AI.