Multiple VPS are installed on one physical server, while a dedicated server is one physical server.
They are both comparable in performance, however VPS are usually cheaper.
Some more things to think about... if you are utilizing the server heavily, a dedicated would be your best choice since VPSs will be sharing the CPU of the physical server. If a bunch of VPSs are heavily used, you may experience some slowness, but usually you get a certain amount dedicated to you, and it is also burstable which can be an advantage.