As someone who uses Vue every day at work I would not say that Vue has a simple API, though it has many conveniences.

I think a fair comparison would be to look at React's component API: https://facebook.github.io/react/docs/react-component.html

And compare it with the Options / Lifecycle Hooks and Instance Properties and Instance Methods sections of the Vue API docs: https://vuejs.org/v2/api/

Vue may be simpler if you have passing familiarity with Angular 1, or if you are very familiar with Mustache-style templates. But I think it's wrong to say the API is simple, or has a small surface.