When should you use rest api for rendering vs server-side rendering?

So hopefully the question makes sense. But I'm needing some guidance. When you are using something like laravel. When should a rest api be used to consume, and display that data using a client-side framework such as vue? Vs using something like blade templates and letting the server-side render the view and just pass the data to the template?

Would be happy to get any guidance on this as im sort of just confused.

Thanks!