How to get visible viewController from app delegate when using storyboard?

This should do it for you:

- (void)applicationWillResignActive:(UIApplication *)application
{
    UIViewController *vc = [self visibleViewController:[UIApplication sharedApplication].keyWindow.rootViewController];
}

- (UIViewController *)visibleViewController:(UIViewController *)rootViewController
{
    if (rootViewController.presentedViewController == nil)
    {
        return rootViewController;
    }
    if ([rootViewController.presentedViewController isKindOfClass:[UINavigationController class]])
    {
        UINavigationController *navigationController = (UINavigationController *)rootViewController.presentedViewController;
        UIViewController *lastViewController = [[navigationController viewControllers] lastObject];

        return [self visibleViewController:lastViewController];
    }
    if ([rootViewController.presentedViewController isKindOfClass:[UITabBarController class]])
    {
        UITabBarController *tabBarController = (UITabBarController *)rootViewController.presentedViewController;
        UIViewController *selectedViewController = tabBarController.selectedViewController;

        return [self visibleViewController:selectedViewController];
    }

    UIViewController *presentedViewController = (UIViewController *)rootViewController.presentedViewController;

    return [self visibleViewController:presentedViewController];
}