Updated snippet if anyone else needs it, with fallback for the legacy ID:
<?php // Check if the event is associated with a Facebook event
$fbid_legacy = tribe_get_event_meta( get_the_ID(), '_FacebookID' );
$fbid_new = tribe_get_event_meta( get_the_ID(), '_EventFacebookID');
if( !empty($fbid_new )) {
$fbid = $fbid_new;
} else {
$fbid = $fbid_legacy;
}
if ( !empty( $fbid ) ) {
// Form and display a link to the FB event page if so
echo '<a class="mt1 tribe-events-button" href="' . esc_url( "http://facebook.com/events/$fbid/" ) .'" target="_blank" rel="nofollow">RSVP on Facebook</a>';
}
?>