These days anyone who is online know there are two popular operating system platforms - Linux and Windows. Even if someone does not know, might have heard about Linux by now :-). On your desktop, it does not make much of a difference as Microsoft Windows is considered the defacto operating system - atleast in India where rampant piracy is there. For many a people only Windows is THE Operating System. But all this changes when  you need to host your website.

So how do your site find its home a.k.a. host. If you are a first time user, it will be your web designer or developer who advices you on what platform you should host. If you are already a developer/designer, who has developed a few sites, will already know what platform to use.  So what should a developer/designer consider while choosing the  hosting type :

1. Web/Application Type - If you require a simple site with no server side scripting and with no databases etc., in that case any platform goes along. Only this that requires due deligence is choice of hosting company.
   
2. Developer Skillset - If your application requires some kind of server side scripting, then a lot depends on your developer's skillset. If you are dealing with a PHP/PERL developer,  you should surely choose Linux (thought both run on Windows also). Primary reason in choosing Linux is that both languages were initially developed/run on POSIX platform (referred for *nix family of OS's inclusing Linux). Also with PHP, MySQL combination is used which is more commonly deployed on  Linux. If your developer us a .ASP or NET developer then you need to go for Windows platform with MS-SQL capability preferrably atleast MS-SQL 2005. 
3. Platform Stability - As far stability is concerned, Linux should be preferred. One can find countless systems admins who will vouch for Linux.
4. Performance - As far performance goes, a lot depends on the hardware used and the application stack being run on it.
   
5. Security -  Though it depends on the platform and by this measure Linux has an edge as it is devoid of most Viruses etc. which are primarily designed for Windows OS. Also earlier version of Windows themselves had many security holes. But other than that, security depends a lot on the system admin. a poorly configured security policy on Linux server, is no better than a Windows machine.
6. Price - Pricewise Linux platform is much cheaper than Windows. Primary reason for this is the License cost on Windows operating system which is passed on to the end user. Also host masters are able to accommodate more sites on a Linux server than Windows server with same hardware specs.

At Pack Web Hosting, we sell both Linux and Windows hosting. For the reasons mentioned above, we do push for Linux somewhat more than Windows. Following Wikepedia article puts more light on this comparison - http://en.wikipedia.org/wiki/Comparison_of_Windows_and_Linux

Now lets come to some trends.

Server trends (source builtwith.com - http://trends.builtwith.com/Server - 10/Mar/2010)

*nix	44.82%
Red Hat Enterprise Linux	23.33%
CentOS	14.76%
Debian	5.07%
Ubuntu	4.23%
Fedora	4.23%
Windows based OS	0.67%%

A small note: Red Hat Enterprise Linux, CentOS, Debian, Ubuntu, Fedora - are various Linux distributions

As per my personal experience and above analysis, I would surely push a client towards Linux hosting.