2 added my sample code
source | link

try this create a page template

<?php
/*
 * Template Name: Compare
 */
?>

<?php
get_header();   
?>


        <form id="customsearch" action="" method="post">
            <select name="compare-one" id="compare-one">
                <option value="130">1</option>
                <option value="102">2</option>
            </select>

            <select name="compare-two" id="compare-two">
                <option value="130">1</option>
                <option value="102">2</option>
            </select>

</form>
<script type="text/javascript">
        $(document).ready(function() {  
            $('#compare-one').change(function() {
                var compareone_value = $('#compare-one').val();
                var data = {
                    'action':'callback_function',
                    'compare-one':compareone_value, 
                };
                $.post(ajax_object.ajaxurl, data, function(response) {
                    $('#compare-one-container').html(response); 
                });
            });

            $('#compare-two').change(function() {
                var comparetwo_value = $('#compare-two').val();
                var data = {
                    'action':'callback_function',
                    'compare-two':comparetwo_value, 
                };
                $.post(ajax_object.ajaxurl, data, function(response) {
                    $('#compare-two-container').html(response); 
                });
            });

        });
</script>              
<div id="compare-container">
    <div id="compare-one-container">

    </div>

    <div id="compare-two-container">

    </div>

</div>

<?php get_footer(); ?>

next add a callback function to your functions.php

add_action('wp_ajax_callback_function', 'callback_function');
add_action('wp_ajax_nopriv_callback_function', 'callback_function'); // for not logged in user
function callback_function() {
if (isset($_POST['compare-one']) || isset($_POST['compare-two'])) {
            $arr_id = array($_POST['compare-one'],$_POST['compare-two']);
            $temp = $wp_query;
            $wp_query = null;
            $wp_query = new WP_Query();

            $wp_query->query(array('post_type' => 'listing', 'posts_per_page' => 2, 'post__in' => $arr_id));
            while ($wp_query->have_posts()) : $wp_query->the_post();
                $custom = get_post_custom($post->ID);
                $beds = $custom['_beds'][0];
                $baths = $custom['_baths'][0];
                apply_filters('the_title', the_title());
                apply_filters('the_content', the_content());
            endwhile;
            $wp_query = null; $wp_query = $temp;
            rewind_posts();

    }
    die();
}
?>

and don't forget to localize WordPress ajax script to use in front page

wp_enqueue_script( 'ajax-script', 'ajax_object', array('jquery'));
    wp_localize_script( 'ajax-script', 'ajax_object', array( 'ajaxurl' => admin_url( 'admin-ajax.php' ) ) ); // setting 

try this create a page template

<?php
/*
 * Template Name: Compare
 */
?>

<?php
get_header();   
?>


        <form id="customsearch" action="" method="post">
            <select name="compare-one" id="compare-one">
                <option value="130">1</option>
                <option value="102">2</option>
            </select>

            <select name="compare-two" id="compare-two">
                <option value="130">1</option>
                <option value="102">2</option>
            </select>

</form>
<script type="text/javascript">
        $(document).ready(function() {  
            $('#compare-one').change(function() {
                var compareone_value = $('#compare-one').val();
                var data = {
                    'action':'callback_function',
                    'compare-one':compareone_value, 
                };
                $.post(ajax_object.ajaxurl, data, function(response) {
                    $('#compare-one-container').html(response); 
                });
            });

            $('#compare-two').change(function() {
                var comparetwo_value = $('#compare-two').val();
                var data = {
                    'action':'callback_function',
                    'compare-two':comparetwo_value, 
                };
                $.post(ajax_object.ajaxurl, data, function(response) {
                    $('#compare-two-container').html(response); 
                });
            });

        });
</script>              
<div id="compare-container">
    <div id="compare-one-container">

    </div>

    <div id="compare-two-container">

    </div>

</div>

<?php get_footer(); ?>

next add a callback function to your functions.php

add_action('wp_ajax_callback_function', 'callback_function');
add_action('wp_ajax_nopriv_callback_function', 'callback_function'); // for not logged in user
function callback_function() {
if (isset($_POST['compare-one']) || isset($_POST['compare-two'])) {
            $arr_id = array($_POST['compare-one'],$_POST['compare-two']);
            $temp = $wp_query;
            $wp_query = null;
            $wp_query = new WP_Query();

            $wp_query->query(array('post_type' => 'listing', 'posts_per_page' => 2, 'post__in' => $arr_id));
            while ($wp_query->have_posts()) : $wp_query->the_post();
                $custom = get_post_custom($post->ID);
                $beds = $custom['_beds'][0];
                $baths = $custom['_baths'][0];
                apply_filters('the_title', the_title());
                apply_filters('the_content', the_content());
            endwhile;
            $wp_query = null; $wp_query = $temp;
            rewind_posts();

    }
    die();
}
?>

and don't forget to localize WordPress ajax script to use in front page

wp_enqueue_script( 'ajax-script', 'ajax_object', array('jquery'));
    wp_localize_script( 'ajax-script', 'ajax_object', array( 'ajaxurl' => admin_url( 'admin-ajax.php' ) ) ); // setting 
1
source | link

Don't really get what your main issue.. are you try to comparing two post types and display it in a page template? or are you try to comparing the current page with the selected post types?