Edit in JSFiddle

var app = new Vue({
    el: '#app',
    data: {
        isEnable: true
    },
    methods: {
    handleClick () {
      this.isEnable = !this.isEnable
    }
  }
})
<div id="app">
    <div v-if="isEnable">v-if</div>
    <div v-show="isEnable">v-show</div>
 <button v-on:click="handleClick">表示・非表示</button>
</div>