Both releases are pretty stable and there is not much to report.
It seems that the biggest news (for Ubuntu) is the shorter life cycle for non-lts versions, and longer cycle (5 years!) for LTS. So the 13.04 release of Ubuntu (Raring Ringtail) will be supported until January of 2014, while 12.04 LTS support extends until April 2017.
Given the relatively minor changes in this release, we would recommend users select Ubuntu 12.04 LTS over Ubuntu 13.04.
Most of the Debian packages get a minor version update from the previous version Debian 6/Squeeze. None are too notable. Examples: MySQL 5.1=>5.5 and PHP 5.3=>5.4.
If you already have a running server and need to upgrade (without reinstalling), see our notes on distribution upgrades please see the following pages for Ubuntu and Debian. Or put in a ticket and let us help you with that.