What is most effective? The benefit of designating two officers is that each can be more specialized, and potentially more effective in their respective areas. However, the risk associated with having two officers is that things that are not clearly just privacy or just security might fall through the cracks if the two do not coordinate well.
Once you've made this important decision, you can begin building a HIPAA compliance policy and procedures around the basic structure you've chosen. (Let me know if you'd like some help with that.) - Matt