Do you split up your content (CMS) and functionality into seperate websites?

I know this *appears subjective and is likely to be closed* but I'll ask anyway.

When you use a CMS for your main website, you always have the ability to extend it to provide rich user functionality, these chunks of functionality may be known as plug-ins or macros etc.

Most of the time I have created user controls which allows editors to drop functionility into the core site amongst the content.

My question is, what is the favoured approach? To keep everything inside the CMS or to split up your content into one site and keep your rich-functionality contained within another site?

A CMS system should separate the engine from the plugins/modules in my opinion. Also, the CMS generated content or resources should only persist within the instance of the environment it runs in. The core engine should never depend on plugins/modules to function.