This really depends.
If the site is newer or is currently on a shared environment, the next natural step is to a VPS. If the site needs its own dedicated environment, it's always possible to upgrade from VPS to a dedicated server once the traffic warrants it.
With a dedicated server you will have full use of the entire server. A VPS is still a shared solution (albeit one with much more flexibility) and resources are shared with other VPS's hosted on the server.
We definitely recommend purchasing the Dedicated server over the VPS if you are ordering new service.
The high level VPS plans are a better solution in some cases, like when you are an existing lower level VPS customer and want a smooth upgrade process while maintaining your existing IP addresses and environment settings.
