While both Linux and Windows may have their advantages and disadvantages, we will only be outlining the key difference between these two operating systems.
Today, Linux is by far the most popular and most widely used operating system in the hosting world. The most popular CMS systems (Drupal, WordPress, and Joomla) are built to run on Linux servers. The most widely used databases in the world (MySQL, MongoDB, and PostgreSQL) are also designed to give out the best performances on Linux-based servers. And the most widely used programming languages have their origins on Linux servers.
The only reason you would need to look at a Windows hosting solution is when you have your application built on Microsoft technology like .NET or MS SQL. These technologies were specifically built for Windows operating systems.
In terms of performance and security Linux takes the lead. There are Linux servers on the "internet" today that have not been rebooted in years, while the same can not be said for Windows solutions. Many developers and system administrators find that it's easier to protect and manage their websites if they're running on a Linux host.