I have a plnkr here that I am testing $scope.$watch on radio buttons with the controller as syntax. In addition, the radio buttons are embedded inside a parent view container.
In the 'About us' page, I have the following html code for showing two radio buttons along with the current selection message:
<div class="row-fluid">
  <div class="well">
    <p><strong>Make a selection:</strong></p>
    <label>Yes</label>
    <input type="radio" name="selection" ng-model="aboutView.radioSelection" value="Yes">
    <label>No</label>
    <input type="radio" name="selection" ng-model="aboutView.radioSelection" value="No">
  <p>{{aboutView.message}}</p>
  </div>
I have the following code in the aboutController.js:
(function() {
  'use strict';
  angular.module('layoutApp')
  .controller('aboutController', aboutController);
  aboutController.$inject = ['$scope'];
  function aboutController($scope) {
    var vm = this;
    vm.radioSelection = "No";  //default selection
    vm.message = "Your selection is " + vm.radioSelection;
    /**
    * **This does not have any response, not working**
    $scope.$watch(vm.radioSelection, function(newVal, oldVal) {
      vm.message = newVal;
    }, true);
    */
  }
}())
Lastly, I have the following block of code in my ui.router config that is relevant to the about us page:
.state('home.about', {
      url: '/about',
      templateUrl: 'about.html',
      controller: 'aboutController as aboutView'
    })
                The following works:
$scope.$watch(
  function() { return vm.radioSelection}, 
  function(newVal, oldVal) {
    vm.message = "Your selection is " + newVal;
  }, 
  true
);
Plunkr
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