The biggest differences between shared and dedicated hosting are going to be space and time.
Space: How big is your site? How much disk space and bandwidth are you currently using? How complicated is your code? Are you planning to host more that one domain?
Shared hosting starts at 200 MB for space and 5GB for bandwidth, dedicated servers start at 60 GB of disk space and 200 GB of bandwidth
Time: How much information are you putting on the server? Do you have a technical admin for your site or company? Are you planning on hosting more than one domain? Who are you planning to have perform the maintenance on your server? Shared hosting, CFDynamics is basically your server admin; we will make space for you to upload your content. Dedicated hosting you are the admin of your server, you are responsible to support that sever thru maintenance, patches and back ups.
FYI: You can purchase Monthly Maintenance on a dedicated server which includes maintenance, patches and back ups, for $200.00 per month.