Why not use PDO instead? You have the benefit of prepared statements amongst other features there and it would prove to be a wise decision should you decide to move to another DB one day.
http://php.net/manual/en/book.pdo.php
If you insist on using one of the options mentioned above, MySQLi is basically a more Object Oriented approach to the standard mysql extension. For the most part, they are functionality-wise the same. If you're building an OOP based application, MySQLi would probably be a wiser, more consistent choice.