The Internet Super Hero blog has posted some statistics comparing the connections per second that can be made with the newly introduced persistent connection support coming with PHP 5.3 in the mysqli (ext/mysqli) driver.
Persistent Connections have been a mixed bag. They can give you a significant performance boost by caching (pooling) connections although MySQL is already comparatively fast at establishing connections. However,connections are stored "as-is" in the cache. They are not "cleaned up".
The ext/mysqli driver takes care of this and a few other problems surrounding the persistent connections by cleaning up things like rolling back active transactions, unlocking tables, closing prepared statements and closing handlers. The trick is in a call to the C-API function mysql_change_user() (= COM_CHANGE_USER).