Series of the cores share common functionality amongst themselves, but the character data structures between them are radically different because of changes in character info between versions (ie, they added achievements in wotlk, and then made them account wide in Cata / MOP), and in MoP / WoD they removed several item slots on certain classes).

The problem with most private servers is not character portability, but scripting portability. A quest scripted for a vanilla core probably won't work on a Burning Crusade one because the API used is different.

The WoW private server scene is actually fascinating to read from a code study perspective, because its all entirely hobbyist and often novice software development. Common solutions to problems like delegation or templates are often unused because the people writing the code just didn't know they existed and never formally studied software best practices.