Both have their own advantages, VPS has its own and dedicated server has its own advantage.
A dedicated server is a standalone server where as when you virtualize a single dedicated server into many sectors, it is called Virtual private server. To take an example, you purchase a hard disc and have not created any drives on it, just one drive, then it is your dedicated server. When you created several drives on hard disk, it becomes a VPS.
In a dedicated server, you can install one OS as there are no other sections where as in VPS you can install more than one OS on different sections.
VPS is suitable for small size business and dedicated server is good for large size business.
Dedicated servers are costly in comparison to VPS.