Nuxt offers a bunch of advantages over plain VueJS, including
- easy Server-Side Rendering (SSR),
- automatic code splitting,
- easier async data, and
- a routing solution with massive reductions in boilerplate.
The downside is that there's no upgrade process to take one codebase from Vue to Nuxt: if you have an existing VueJS app of any size, you'll have to create a fresh Nuxt app and then port it all over.
However, this isn't quite as bad as it seems at first -- your Components and Vuex stores won't have to change much if at all, and everything else you could do in Vue has an equivalent in Nuxt.