World space means it uses the same global axis everywhere. Local space means it regards the axis as if they were part of the game object, so when you rotate the parent then you also rotate the child so the local axis will also change.
I've asked around and there seems to be no default axis for the parent rotation. However, you can use inverse direction transform (or whatever it's called in. Playmaker) and convert a local vector to a world position based on another game object. Then you can use that in a world transform action for example.
An integration of this into actions like translate may b useful, but it ,may also confuse new users, so I dunno if it might be a good thing.
Well, at least now you know how it could be done if wanted to integrate it yourself. Hope it helped and I'm not misunderstanding stuff :-)