Your choice of server platforms should be dictated by the use to which you intend to put it. The majority of web features run fine on both platforms including PHP, mySQL, POP3 etc. If you intend to create your site using ASP, FrontPage, the .NET environment, Windows Streaming Media, Access, MSSQL, or any of the other Microsoft proprietary technologies then you probably need to use a Windows host. There is limited support for a number of these technologies in Linux, but they can be expensive and are usually lacking in features. It is probably worth considering the fact that if you use server specific technologies and then change hosts you'll have a much harder time of it than if you use technologies that can be run on any system. Having it run generic technologies removes the need to focus on specifics and allows you to focus on the quality of service itself.
The reliability and stability of the different platforms have been the topic of many long arguments. The main reason that Windows is seen as being insecure is that it is the most widely used operating system for home PC's. People spend more time looking for flaws in the most common system. With Linux being the most common server type, it has a surprising number of successful hack attempts made on it. In the end the security of both platforms comes down to the competency of the system administrators. If you are security minded then you'll do better to make sure that the hosting company is reputable and highly skilled than to worry about the server they use.
In terms of performance there's not a huge difference between the two servers. Linux reportedly performs faster because Windows (as usual) attempts to offer an 'all in one' package instead of the extendable Linux implementation. You'll generally not notice a difference but if performance is of utmost importance to you then maybe this will influence your decision.
