Both Windows and Linux offer unique advantages to hosting. Technically there is no visible difference to the end user (the person browsing your website) if you use Windows or Linux hosting. Both offer premium uptime, reliability, and security. The real differences are on the back end in which you develop the site.
The place where Linux differs distinctly from Windows hosting is in the area of development tools amd server technologies. If you're writing scripts in ASP or ASP.NET, you need Windows hosting. Similarly, MS-SQL databases, Access databases, the newer version of Frontpage Server Extensions, and other specific Microsoft tools are only available with the Windows hosting plan.
Both Windows and Linux hosting plans allow you to use Perl, PHP, MySQL databases, CGI scripts etc.
Go for Microsoft for more advanced features. Go for Linux on price.