It was a very difficult question, because:
* In US was probably best factories and very good sources of materials. Also US has had a very nice radial engines and using of turbo supercharger has had great influence.
* In England was very good inline engines and sleeve valve radials, but had a some lack of manufacturing equipments and materials due bombing raids. Also in my opinion RR get a best influence of centrifugal supercharges in Merlin engine. Developed also very compact H-24 and X-24 engines.
* In Germany was absolutely best technical innovations, but also has had a lack of materials and manufacturing facilities. Also lack of hi-grate fuel caused lack of engine performance. Was only one country in WWII era with rocket and jet engines in military use.
* In Japan was very high productivity of engines, but lack of own innovation. Also if I has understand correct, lack of proper carburettor designs caused some performance lost of engines.
* In Russia it was generated lot of improvements of copied US and France engines, but don't have actually any good own engine design and every engines based on design before war era.