var app = angular.module('app', ['ui.bootstrap']);

angular.module('app').service('MyService', function() {
    this.doStuff = function(date) {
        console.log(date);
    }
});

angular.module('app').config(function($provide) {
    $provide.decorator('datepickerDirective', ['$delegate', 'MyService', function($delegate, MyService) {
        var directive = $delegate[0];

        var link = directive.link;

        directive.compile = function() {
            return function(scope, element, attrs, ctrls) {
                link.apply(this, arguments);

                scope.$watch(function() {
                    return ctrls[0].activeDate.getMonth();
                }, function() {
                    MyService.doStuff(ctrls[0].activeDate);
                });
            }
        };
        return $delegate;
    }]);
});