A functional component is not pure, it's exactly the same as its class counterpart. You can use recompose's[0] 'pure' HOC to turn it into a PureComponent.
I believe their question is asking about the trade-offs of a PureComponent, which is a Class and incurs a performance hit because of that versus a functional component which is always faster than the equivalent component written in a Class-y syntax.
I.e., do the gains from PureComponent exceed the cost of a Class? Personally I would assume they would otherwise no one would ever think of think using one, but it is an interesting question and set of metrics that could be gathered.
Not sure I understand your question. Functional components and class components both use createClass internally IIRC. In any case, they are the same. A PureComponent is simply a Component with shouldComponentUpdate written for you. Functional components can't be pure, but you can use an enhancer for them.
e.g.,
vs