Yep, it is fine to upgrade BPS. I should have been a little more specific about what MySQLi vs MySQL means exactly, but I kept it short so not to clutter up the Upgrade Notice.
MySQLi is better for security and it has the benefit of having all sorts of pre-built object oriented things. MySQLi has been available since PHP5.x so all hosts will have this. MySQLi class/functions connect to MySQL Databases the same as the older php mysql_xxx functions do.