Send a confirmation of user role upgrade conditionally

I’m using this snippet of code to send a confirmation email to user’s when their account is upgraded to a new user role.

function user_role_update( $user_id, $new_role ) {
    $site_url = get_bloginfo('wpurl');
    $user_info = get_userdata( $user_id );
    $to = $user_info->user_email;
    $subject = "Role changed: ".$site_url."";
    $message = "Hello " .$user_info->display_name . " your role has changed on ".$site_url.", congratulations you are now an " . $new_role;
    wp_mail($to, $subject, $message);
}
add_action( 'set_user_role', 'user_role_update', 10, 2);

This sends an email whether the account has been upgraded or downgraded which doesn’t give me the flexibility of sending a different message for a downgrade. I have two situations where this is used.

1. When a user is upgraded from “contributor” to “author”.
2. When an “author” is downgraded to “contributor”.

How can I use conditions to send a different email for each of these events?

Quite possibly something like this might work;

    function user_role_update( $user_id, $new_role ) {
    $site_url = get_bloginfo('wpurl');
    $user_info = get_userdata( $user_id );

    if (user_can( $user_id, 'capability' ) ) {

        $to = $user_info->user_email;
        $subject = "Role changed: ".$site_url."";
        $message = "Hello " .$user_info->display_name . " your role has changed on     ".$site_url.", congratulations you are now an " . $new_role;
        wp_mail($to, $subject, $message);

    } elseif (user_can( $user_id, 'capability' ) ) {

    // etc...

    }

}
add_action( 'set_user_role', 'user_role_update', 10, 2);