| One of my references describes the Nakajima Ki-44 Shoki (its Japanese name, meaning "Demon") as "an effective fighter, fast-climbing and manouverable".
However, it served almost entirely as a Home Defence fighter, with just a few serving in Burma and New Guinea, so it may not have encountered the Allied fighters that you mention that much. It is said to have been effective against formations of B24 Liberator bombers.
Sorry I don't have anything more specific. |