If you have a main website (www.example.com) with a subdomain of the website (service.example.com) that lives on a separate server with a separate IP address, is there an SEO benefit/advantage to have having the www included in the url since the parent url includes the www?
Assume:
1. Applicable 301 redirects are in place on both sites
2. No duplicate content issues
Additionally, would your answer be different if the site is a .gov or .edu site vs. a .com?