Strangely enough WordPress has no function for checking whether a page has children/subpages. This has to be checked using a somewhat more cumbersome method as highlighted below:

$children = get_pages('child_of='.$post->ID);?>
if( count( $children ) != 0 ) { // Has Children }
else { // No children }

OR

$children = wp_list_pages('&child_of='.$post->ID.'&echo=0');
if($children) {
    // This page has subpages
}

If anyone knows of a better way to do this I’d be interested to know. Until then, this is probably the best way to check whether a page has children or subpages.