In terms of SEO is there any benefit about using Google SiteSearch over internal search (eg. Wordpress' own search engine)?
Not directly. They both will find your content (although Wordpress will find it faster since it knows about the content immediately whereas Google has to find it and index it first) and display it to your users. And neither affect your rankings since neither affect your content.
The only possible advantage I see from using Google SiteSearch is it forces Google to crawl your site more frequently and deeply as they need to make sure they know about all of your content in order to deliver useful search results. Obviously doing this for site search means they can use the same information in their main search results which is a good thing.
I just use both with this custom addition to the theme's search.php file:
<div id="googleResults"> <h2>Google Search</h2> <iframe id="gcs" src="<?php $url_iframe .= 'http://www.google.com/cse?'; $url_iframe .= 'title=Search_Results&'; $url_iframe .= 'cx=' . $google_code_cx . '&'; $url_iframe .= 'cof=' . $google_code_cof; $url_iframe .= 'q=' . urlencode( get_search_query() ) . '&'; $url_iframe .= 'sa=Search&'; $url_iframe .= 'siteurl=' . urlencode($_SERVER['HTTP_HOST'] . $_SERVER['REQUEST_URI'] ) . '&'; $url_iframe .= 'ad=w9&num=10'; echo htmlspecialchars( $url_iframe ); ?>"></iframe> </div>