From what I learned here, upgrading your server from VPS to dedicated all depends on your traffic and needed resources. If your website is slowing down already because of traffic then you might need faster applications or bigger data space for storage. Then that might be the time to upgrade from VPS to Dedicated.
It is also a wise idea to consult your web hosting company if you need to upgrade. Sometimes there are just some problems that needs to be solve and upgrading is not the solution.
If you want to compare between VPS and Dedicated, here is the physical evidence: (click the links to see the comparison)
Virtual Private Server (Fully Managed Virtual Private Servers Starting at $24.99USD p/m Only at BODHost.com)
Dedicated Servers (Fully Managed Dedicated Servers - 100% Guaranteed Uptime only at BODHost)