How to tell which bootstrap tab is selected in Angular-UI

Actually this is really simple as each pane exposes the active attribute that supports 2-way data binding:

<tabs>
    <pane ng-repeat="pane in panes" heading="{{pane.title}}" active="pane.active">      
        {{pane.content}}
    </pane>
</tabs>

and then an active tab can be easily found, for example:

$scope.active = function() {
    return $scope.panes.filter(function(pane){
      return pane.active;
    })[0];
};

Here is a working plunk