as always it depends :D
In generell I would say the API approach is better, espacially in the long run with different teams working on the frontend and backend with different technologies, approaches and speed. The only think they need to agree on is the API structure. So if this is defined both teams can start developing without the real implementation is done by using API mocks. And also the reusability of the API is great, consider mobile apps, open some resources of the API to the public, enable white label solutions and so on. Also you can change the backend technology completly without changed one line of the frontend, as long as the API interface stays the same.
But in the beginning if a project the setup of the CI process, choosing the rechnologies, preparing the structure, etc. pp. for both parts is more complex and time consuming then for monolithics. So if you phasing time pressure or just want to build a prototype you properbly faster with a traditional way of building the web app. Always consider refactor the project to a API approach later ;)