Same user for multiple sites
Sounds like Bakery module would meet the requirements for you. It will handle single sign-on between Drupal sites on different sub-domains.

As far as performance goes, Bakery is used by drupal.org when you switch between https://www.drupal.org, https://groups.drupal.org, https://assoc.drupal.org and others. 

What it doesn't do is to switch between different domains like drupal.org and drupal.com. Bakery also doesn't sync user information, if you have user fields.

For more advanced features like SSO between Drupal and non-Drupal, look at CAS module, or some of the other single sign-on solutions.