The two are generally the same. Both use PHP, MySql databases, and many more. Many people believe that if they are using a Windows based operating system, they have to use a Windows based hosting. But that is not always the case. Most people with Windows based operating systems prefer to use Linux based hosting to Windows based hosting.
Windows is better for hosting files created using Windows based technology. For example, if you created a web site in html using Windows FrontPage, or used ASP or the .net environment, or any other Windows program to create your site, then you should choose Windows based hosting.
When it comes to security, there is basically no difference between the two. It pretty much all depends on the hosting company you used and the plan you signed up for. Both of the applications have been hacked.
In general, your Windows has been found to be more insecure than Linux.
Now if you are still a little bit unsure of which direction to go in, a suggestion would be to call up your hostŐs support number or send them an email with an outline of exactly what you plan to host and what the features of your site are.
The bottom line is, if you used a Windows program to create your site, then use Windows based hosting, if not, then go with Linux.