For me Vue.js is like a light-weight Angular 1, in a good way. It's very intuitive and you can start working immediately. It does however easily end up in confusion about where the state lives with the two-way binding. I've run into a lot of implicit state changes wrecking havoc. The declarative nature of React definitely wins here, especially working with stateless functional components. If you're serious about Vue you should adhere to unidirectional bindings, components and use Vuex.
The best thing about Vue.js for me is the single file components. It's such a nice feeling to know that everything affecting a certain component is right before your eyes. That's also the reason I started adapting CSS-in-JS in my React components.
The biggest problem for me with Vue.js is the template DSL. You often think "how do I do this complicated tree render in Vue's template syntax? In JSX I would just use JavaScript". For me, that was the best upgrade going from Angular to React and it feels like a step backwards when using Vue.js.