passing argument to get_template_part() or a better way to code

Why don’t you use a simple function with an argument to achieve that, the code is something like this:

function wpse63585_event_list( $fresh = true )
{
    echo '<ul class="event-items">';

    $yesterday = time() - 24*60*60;
    $compare = $fresh ? '>' : '<';

    $args = array(
        'post_type' => 'wr_event',
        'posts_per_page' => -1, // show all posts
        'meta_key' => 'event_date',
        'orderby' => 'meta_value_num',
        'order' => 'ASC',
        'meta_value' => $yesterday,
        'meta_compare' => $compare,
    );

    $loop = new WP_Query( $args );
    while ( $loop->have_posts() ) : $loop->the_post();
        get_template_part( 'inc/event', 'item' );
    endwhile;
    wp_reset_postdata();
    echo '</ul>';
}

And then in your index.php, just call:

<?php wpse63585_event_list(); ?>

and in archives.php:

<?php wpse63585_event_list( false ); ?>

Another solution I can think about is you can register a global variable, like $wpse63585_fresh = true, and use that variable in your template part event-list.php to control the condition, like this:

In index.php:

global $wpse63585_fresh;

$wpse63585_fresh = true;
get_template_part( 'inc/event', 'list' );

In archive.php:

global $wpse63585_fresh;

$wpse63585_fresh = false;
get_template_part( 'inc/event', 'list' );

In event-list.php:

<ul class="event-items">
<?php
    global $wpse63585_fresh;
    $compare = $wpse63585_fresh ? '>' : '<';

    $yesterday = time() - 24*60*60;
    $args = array( 
        'post_type' => 'wr_event', 
        'posts_per_page' => -1, // show all posts 
        'meta_key' => 'event_date', 
        'orderby' => 'meta_value_num', 
        'order' => 'ASC',
        'meta_value' => $yesterday,
        'meta_compare' => $compare           
    );

    $loop = new WP_Query( $args );
    while ( $loop->have_posts() ) : $loop->the_post();
        get_template_part( 'inc/event', 'item' );
    endwhile;
    wp_reset_postdata();
?>
</ul>