The two biggest difference between them I've noticed is that Vue has been more "batteries included". The Vue authors have made all the choices (and integrations) around routers, state management etc for you. If you like the decisions they've made then that's great, if you don't then you might find yourself using less polished libraries.

The other is what I think has lead to Vue's popularity, that is, it allows you to get away with more and not in a good way. React makes it quite hard to deviate from their model of doing things. I.e. state flows down via props and back up via callbacks. However, with Vue, it's quite possible for components to know (and interact) with their parent components directly, i.e. call methods on them, modify internal state. This makes it easy to get things going but leads to all sorts spaghetti code down the track. React does its best to stop this kind of behaviour.

In summary, Vue has gained traction not only from it batteries included approach (and being novel) but also because it allows you less frustration when developing and doesn't try to stop you from writing terrible code like React does.