Does anyone have any particular reasons to do this either way?

I'd lean towards the 'dummy' method approach for a few reasons:

• I try and make the 'normal' control flow of a method be as obvious as possible (illuminate the mainline). Having that if-statement there makes the code little bit harder to parse, and most of the time it will be unnecessary.
• If I need to ensure that sub-classes override _Private_X I can make the base-class's implementation die and get a runtime error if I forget to override it in the subclass
• If I later decide that I need some _Private_X behaviour in the base class I have somewhere to put it.
• Including the method present in the base class makes the interface of the class easier for the casual reader to understand.

I'd also not use the leading underscore convention for this method. Since it's intended to be overridden in sub-classes I'd look upon it as part of the public API rather than something private.

Or some other way?

Depending on the application it might make sense to delegate the _Private_X behaviour to another subroutine or object. For example if you wanted different _Private_X behaviour on a per-object rather than a per-class basis, or if the behaviour was conceptually separate and might be reused in different sub-classes.