MySQLi is a “new” and improved version of the original MySQL extension for PHP. While there is no especially convincing reason to switch from the original MySQL functions to MySQLi, both MySQL and PHP recommend that developers do so.
WordPress is aimed for the masses and WordPress 2.0 still supports even MySQL 3.x — so most likely we won't be seeing a switch to a MySQLi-powered WordPress anytime soon. However, for those that care about such things, we've created a MySQLi conversion file for WordPress.
In our testing, MySQLi processed queries and page loads at around a couple of microseconds slower or faster than the normal MySQL functions depending on the queries being issued and the current load on the server (MySQLi seems to perform better under heavy CPU load than MySQL). MySQLi is more reliable under times of PHP load, but isn't any faster or better performing as far as MySQL is concerned.