I tried all of them and now I'm using Vue because:
React: It was good to play with but personally I hate the jsx syntax (html surrounded by parenthesis). I prefer to separate different languages/markups. I know it hardly can be a valid reason but my feelings important to me :) Another point was its license and all restrictive conditions behind the scenes - have you ever read it?
Angular (v2): I started to learn Angular 2 from the very beginning. I was very excited until they introduced their own "module system" around the RC5. After lot of breaking changes during the "RC" period which was also annoying to follow. There was a huge thread on github about why this new architecture is a mess. I checked recently and they solved the modularity problem somehow. Maybe I will check it (v4?) again later. Another point is I think typescript is unnecessary at all. We have ES6/7 today and there are linters. No need another layer. As a summary I think Angular is more like a huge, complicated ecosystem rather than a simple framework. It means it force you to learn a lot before you get any real result.
Aurelia: It was not listed here but the next one was it to me. I quickly get rid of it after realized the business plans behind the scenes. They decided to provide all really useful parts (reusable UI components) only for subscribers.
Vue2: After the journey with React, Angular 2 and Aurelia and after I dropped all of them I was looking for a simple, easy to learn lib. Fortunatelly the new v2 version of VueJS was just released then. So I gave a shot and I was amazed how easy was to learn and how productive I became. Since I tried all others above I was able to compare all strengths and weaknesses based on my personal experience - instead of someone else's thoughts. As a summary I think the best reason to use Vue is it provide a way to create a dead simple apps by few lines of code and also allows to create a huge, complex solutions. You can learn it step by step at your speed and you will get outstanding result from the very beginning.