I really don't think there is any great advantage by WW 2 one way or the other and that the WW 1 distinction between a battleship and a battlecruiser was no longer relevant.
The speed advantage of the battlecruiser that existed in WW 1 really had diminished to virtually nothing by WW 2. Battleships were now doing 25 to 30 knots just as the remaining battlecruisers were. Tactically, speed is of virtually no advantage in a surface action with regard to battleships / battlecruisers in WW 2. So, any slight advantage in speed a battlecruiser possessed in WW 2 was tactically irrelevant. Cruising range and cruising speeds on the other hand were very significant.
As for armor and or gun power this too was becomming more and more blended to a point where there was little to choose between the two. Yes, there were older battlecruisers that had weak armor and or armament relative to newer ships but, they were still quite capable in many roles as capital ships.
As an example the two weak capital ships Repulse and Reknown proved very useful as carrier escorts and in operations in general. The Reknown at the Lofoten Islands in 1940 fought both Scharnhorst and Gneisenau successfully even though out matched in guns and armor. So, it is possible for a ship with limited capacity on paper to do quite well in actions where other factors give the advantage.