Dynamic Sidebars On Multiple Subpages

More easy & elegant (higher maintainability):

<?php 
// Your sidebar should have the wp_meta action hook
wp_meta();

// in ex. your functions.php
function my_sidebar_content() {
    // "About" Page
    if ( is_page('about') ) {
        // If some widget is added via Admin > Design > Widgets
        if ( is_active_sidebar( 'widgets-sidebar-default' ) ) {
            // Display Widgets
            dynamic_sidebar( 'widgets-sidebar-default' );
        }
        // Default Content before Widgets were added
        else {
            _e('default static content', TEXTDOMAIN);
        }
    }
    // "Links" Page
    elseif ( is_page('links') ) {
        if ( is_active_sidebar( 'widgets-sidebar-links' ) ) {
            dynamic_sidebar( 'widgets-sidebar-links' );
        }
        else {
            _e('default static content', TEXTDOMAIN);
        }
    }
}
add_action( 'wp_meta', 'my_sidebar_content', 10 );

# ===================================================
// OR:
wp_meta();

// functions.php
function load_my_sidebars() {
    // "About" Page
    if ( is_page('about') ) {
        get_template_part( 'sidebar_content', 'default' );
    }
    // "Links" Page
    elseif ( is_page('links') ) {
        get_template_part( 'sidebar_content', 'links' );
    }
}
add_action( 'wp_meta', 'load_my_sidebars', 10 );

// in sidebar_content-default.php
    // If some widget is added via Admin > Design > Widgets
    // You can add any static content right here before the widgets
    if ( is_active_sidebar( 'widgets-sidebar-default' ) ) {
        // Display Widgets
        dynamic_sidebar( 'widgets-sidebar-default' );
    }
    // Default Content before Widgets were added
    else {
        _e('default static content', TEXTDOMAIN);
    }
    // You can add any static content right here after the widgets

// in sidebar_content-links.php
    if ( is_active_sidebar( 'widgets-sidebar-links' ) ) {
        dynamic_sidebar( 'widgets-sidebar-links' );
    }
    else {
        _e('default static content', TEXTDOMAIN);
    }
?>