It is a purely business decision. Using a framework leads generally to less code and faster development. Not using a framework leads generally to more control over what website is doing and better performance.
In practice, the rule doesn't work very well in every circumstance.
- If your team doesn't know anything about a framework you want to use, you're screwed.
- If your team doesn't know the language very well, chances are things will be slower then when using a framework.
- If the website is very small, I'm not sure if using a framework will reduce the quantity of code to write.
In general, I would recommend not using a framework for small-scale websites, use framework for medium-size websites, and write your own framework for large-scale websites.
This said, it might be an exception in PHP. The language is so poor, that it makes sense to use the framework even for small-scale websites to abstract some of the stupidities and lacks of PHP. Also, when developing a small website, you rarely know that it will stay small forever; using a framework from the beginning let you to better manage scalability and to avoid to have to rewrite everything from scratch to migrate from pure PHP to a framework later.