Wrong. Not if the same RPM is maintained. The efficiency is thrust HP over BrakeHP. Since the higher pitched prop will have more thrust it will have greater efficiency. You might be right if we are talking about a static condition, but at speed the lower pitched large prop will be near its max and have very little thrust thus little efficiency. I think you are confusing using smaller props of near the same pitch, where the smaller diameter allows the engine to speed up and thus has more friction loss and little improvement in angle of attack. But in this case we are keeping the RPM the same and the higher pitched prop will have more thrust.