If you're a new or casual Webmaster and your site is non-revenue generating with static HTML pages you generated from boxed software, you probably are hosted on a Linux server. This is the best solution overall for you because Linux hosting costs less and you hardly ever need to delve into the more advanced functions. Server operating system becomes a non-issue. All you need to do is to have a good host. You might want to visit HostVoice (link: http://hostvoice.net) to find one.
The moment you decide you want your site to have more complex features like members only area, e-commerce, live help and so on, then the server operating system might be important. Interactive features rely on server side programs that process your site visitor's input and returns something intelligent. There are many programs out there but most common are ASP, PHP and Perl.Windows Desktop And Server Operating System
Just because you run a windows desktop doesn't mean you must opt for Windows web hosting. This is true vice versa. Whatever operating system you use on your desktop has little to do with your choice of hosts. As long as you understand your FTP or web publishing software, your host can be any operating system.Website Objectives
What is important however is you know what you want your site to do, what you want to offer on your web site. This is what will ultimately lead you to the type of hosting. As mentioned before, interactive sites usually rely on ASP, PHP or Perl type languages. Each programming language has it's own strengths and weaknesses and sometimes one can give you something the other can't although not very often. PHP and Perl are Linux based and ASP Windows.
If you opt to use ASP to power your web site, then you'll want to go with Windows hosting. You might be told that ASP is available on Linux hosting packages and that is true. But bear in mind it might not work as well on Linux as they would on Windows. This is also true the other way around. While you can have PHP or Perl on a Windows web host, they weren't developed for Windows and might not work as well. In fact, there are often disclaimers about using these languages on Windows servers.
Some hosts have successfully implemented these programming languages for the different platforms. Be very clear in this case about the scripts you want to use because server configurations for Windows can be vastly different from Linux. This might cause the script to fail or not function at it's full potential. It's always best to go with the operating system the language was built for.Security
You'll most likely be told flatly Unix based servers have better security. Mainly because these operating systems have consistently been reliable while Windows is a big target for exploitation. Hosting wise it boils down to one thing. No matter how secure the operating system is, your site cannot be secure if your host has not configured it correctly and isn't updated often or swiftly.
In speed and performance they both perform well. Hardware is a big factor here. Again, look to your host. Do they upgrade well ahead or do they max out the resources before doing so?
In conclusion, the key that decides if you should have a Windows or Linux host is what you want your site to do now and in the foreseeable future.