Angular UI Bootstrap Vertical Tabs

This fiddle implements what you need:

https://jsfiddle.net/GetUIKit/b3nhjvot/

 <div class="col-xs-9">
          <!-- Tab panes -->
          <div class="tab-content">
            <div class="tab-pane active" id="home-vr">Home Tab.</div>
            <div class="tab-pane" id="profile-vr">Profile Tab.</div>
            <div class="tab-pane" id="messages-vr">Messages Tab.</div>
            <div class="tab-pane" id="settings-vr">Settings Tab.</div>
          </div>
        </div>

        <div class="col-xs-3"> <!-- required for floating -->
          <!-- Nav tabs -->
          <ul class="nav nav-tabs tabs-right sideways">
            <li class="active"><a href="#home-vr" data-toggle="tab">Home</a></li>
            <li><a href="#profile-vr" data-toggle="tab">Profile</a></li>
            <li><a href="#messages-vr" data-toggle="tab">Messages</a></li>
            <li><a href="#settings-vr" data-toggle="tab">Settings</a></li>
          </ul>
</div>

Switch between tabs can be done as it is explained in Sergey's answer

Another solution is to create something like this

<div class="row">
<div class="col-sm-3">
    <ul class="nav nav-tabs nav-stacked nav-pills" role="tablist">
        <li ng-class="{'active': view_tab == 'tab1'}">
            <a class="btn-lg" ng-click="changeTab('tab1')" href="">My Tab 1</a>
        </li>
        <li ng-class="{'active': view_tab == 'tab2'}">
            <a class="btn-lg" ng-click="changeTab('tab2')" href="">My Tab 2</a>
        </li>
    </ul>
</div>
<div class="col-sm-9">
    <div class="tab-content">
        <div class="tab-pane" ng-show="view_tab == 'tab1'">
            This is tab 1 content
        </div>
        <div class="tab-pane" ng-show="view_tab == 'tab2'">
            This is tab 2 content
        </div>
    </div>
</div>
</div>

And how in JS

$scope.changeTab = function(tab) {
    $scope.view_tab = tab;
}

In approach like this I have more control over HTML markup.

In order to implement those tabs, we need to do a couple of things.

1. Add 'tabs-left' css class to angular ui bootstrap tabs as referenced from https://github.com/angular-ui/bootstrap/issues/102

   <tabset class="tabs-left">
       <tab heading="Vertical A">Vertical content A</tab>
       <tab heading="Vertical B">Vertical content B</tab>
   </tabset>
   

2. Add the custom css as answered from Stacked Tabs in Bootstrap 3

   .tabs-below > .nav-tabs,
   .tabs-right > .nav-tabs,
   .tabs-left > .nav-tabs {
       border-bottom: 0;
   }
   
   .tab-content > .tab-pane,
   .pill-content > .pill-pane {
       display: none;
   }
   
   .tab-content > .active,
   .pill-content > .active {
       display: block;
   }
   
   .tabs-below > .nav-tabs {
       border-top: 1px solid #ddd;
   }
   
   .tabs-below > .nav-tabs > li {
       margin-top: -1px;
       margin-bottom: 0;
   }
   
   .tabs-below > .nav-tabs > li > a {
       -webkit-border-radius: 0 0 4px 4px;
       -moz-border-radius: 0 0 4px 4px;
       border-radius: 0 0 4px 4px;
   }
   
   .tabs-below > .nav-tabs > li > a:hover,
   .tabs-below > .nav-tabs > li > a:focus {
       border-top-color: #ddd;
       border-bottom-color: transparent;
   }
   
   .tabs-below > .nav-tabs > .active > a,
   .tabs-below > .nav-tabs > .active > a:hover,
   .tabs-below > .nav-tabs > .active > a:focus {
       border-color: transparent #ddd #ddd #ddd;
   }
   
   .tabs-left > .nav-tabs > li,
   .tabs-right > .nav-tabs > li {
       float: none;
   }
   
   .tabs-left > .nav-tabs > li > a,
   .tabs-right > .nav-tabs > li > a {
       min-width: 74px;
       margin-right: 0;
       margin-bottom: 3px;
   }
   
   .tabs-left > .nav-tabs {
       float: left;
       margin-right: 19px;
       border-right: 1px solid #ddd;
   }
   
   .tabs-left > .nav-tabs > li > a {
       margin-right: -1px;
       -webkit-border-radius: 4px 0 0 4px;
       -moz-border-radius: 4px 0 0 4px;
       border-radius: 4px 0 0 4px;
   }
   
   .tabs-left > .nav-tabs > li > a:hover,
   .tabs-left > .nav-tabs > li > a:focus {
       border-color: #eeeeee #dddddd #eeeeee #eeeeee;
   }
   
   .tabs-left > .nav-tabs .active > a,
   .tabs-left > .nav-tabs .active > a:hover,
   .tabs-left > .nav-tabs .active > a:focus {
       border-color: #ddd transparent #ddd #ddd;
       *border-right-color: #ffffff;
   }
   
   .tabs-right > .nav-tabs {
       float: right;
       margin-left: 19px;
       border-left: 1px solid #ddd;
   }
   
   .tabs-right > .nav-tabs > li > a {
       margin-left: -1px;
       -webkit-border-radius: 0 4px 4px 0;
       -moz-border-radius: 0 4px 4px 0;
       border-radius: 0 4px 4px 0;
   }
   
   .tabs-right > .nav-tabs > li > a:hover,
   .tabs-right > .nav-tabs > li > a:focus {
       border-color: #eeeeee #eeeeee #eeeeee #dddddd;
   }
   
   .tabs-right > .nav-tabs .active > a,
   .tabs-right > .nav-tabs .active > a:hover,
   .tabs-right > .nav-tabs .active > a:focus {
       border-color: #ddd #ddd #ddd transparent;
       *border-left-color: #ffffff;
   }