One of webpack benefits is that you can make module available in all of your files. In Vue.js we talk in components. So what you did is that you use jQuery module in you component and it will be available only in that component. To make it global add to your webpack config file:
webpack.base.conf.js
var webpack = require("webpack")
module.exports = {
  plugins : [
        new webpack.ProvidePlugin({
            $ : "jquery",
            jQuery : "jquery"
        })
  ],
};
simple configuration webpack config file. Now jQuery will be available in all of your components, and now component looks cleaner: 
Vue component
<template>
   <input type='checkbox' id="toggle-checked" v-model="active">
</template>
<script type="text/babel">
      require('bootstrap-toggle')
      export default {
        data () {
          return {
            active: 1
          }
        },
        mounted: function () {
          $('#toggle-checked').bootstrapToggle()
        }
      }
</script>
This approach is good for a complex web apps with many assets such as CSS, images and other loaders, and Webpack will give you great benefits. But if is your app small Webpack will be overhead.