Height, boarding, and the turtle ship's roof

Did Korean ships have a height advantage over Japanese ships?

Not generally. Their heights were broadly comparable, and some Japanese ships were better suited to boarding, which helped make the turtle ship's roof valuable.

There was no simple Korean height advantage. The fleets' ships were broadly similar in height, although some Japanese vessels gained local advantages and were regarded as better boarding platforms. That mattered because Japanese troops preferred close combat while Korean tactics depended on preserving artillery range. The covered turtle-ship deck therefore answered a boarding threat rather than merely making the vessel look armored.