MCE 2005 is really neither. The actual OS install disk, CD1 is XP Pro SP2. However, when you use the second CD to install MCE2005, it changes or disables certain things in the initial install. It does not officially allow you to join a domain, because that would break the fast user switching functionality that is necessary for media center extenders. The only way to get a MCE2005 box on a domain is to upgrade a MCE2004 machine that is already a member of a domain. If you do a clean MCE2005 install, or upgrade a machine that is not already on a domain, the option to join is not available. Also, upgrading a MCE2004 domain member to MCE2005 will break the media center extender features.
However, MCE2005 DOES have remote desktop, which Home does not. It also supports EFS, multi-processor machines, IIS and dynamic disks, all Pro-only features.