There is no big difference in the PHP language level.
- libmysqlclient distributed by MySQL, mysqlnd distributed by PHP.
- libmysqlclient is part of MySQL, you need install MySQL library.
- Their license are different.
- mysqlnd supports a lot of plugins (mysqlnd_ms & mysqlnd_qc & ...).
- Because mysqlnd is part of PHP, its memory could be limited by PHP configuration.
- mysqlnd is the default after 5.4
http://php.net/manual/en/mysqlinfo.library.choosing.php