A Linux Server provides you with more flexibility, resources and speed. A shared web hosting service shares all resources and speed across the users on the shared hosting platform. You will be able to install and run any special requirements you may need for your website or applications. You won't be sharing a server with thousands of other websites, so the Linux Server is dedicated to run anything you want, super fast!
Servers are the better option for large, high-traffic sites as well as resource-intensive web applications. If you have outgrown your Web Hosting, then you might need a server.