WWII, as with most wars, was an amazing technology leap. In only seven years, aircraft went from not much more than biplanes (even some of them participated) to jet and rocket powered planes. The different types of aircraft that was developed was stunning. Airplanes were designed, built and flew in months. The side that is perceived to be at a disadvantage usually is the most creative, the side with the advantage tends to be Conservative or reactive. After WWI, Germany was limited in its military growth so it spent it effort in tactics and weapons quality and as a result, was significantly ahead in tactical warfare theory and application (but behind in strategic theory and application). With initial success, Germany put technology on a lower burner (attrition replacement was given a priority) and projects like jet power was let to wander. The Allies at this time, after years of ambivalence over the military, struggled hard to catch up (some technology such as the spit and some tanks were equivalent but in insufficient numbers). After the allies gained the advantage, an increasingly desperate Germany turned again to technology to save them. The allies, with more men and material, emphasized attrition replacement and applied statistical theory to warfare (if I build twice as many tanks that are half as good as the enemy, I will win). This led to things like the Sherman tank, which was not even half the capability of the enemy but just swamped them in numbers. The theory works, its just bloody. The allies at this time was strictly reactive and built tons of producible, and capable, aircraft. When the jet appeared, the allied reacted. When the V-1 appeared, they reacted, etc.
Mathematical theory won.
After all this baloney, the point is, there is no argument for the allies being ahead of Germany in areas or aerodynamic theory and aircraft and missile design at the end of the war. All allied nations changed their aircraft and missile (if they had any) designs to accommodate the information captured from the Germans. Had the allies been at a disadvantage, the reverse would have been true. From my perspective, the technological levels of the allies and axis was equivalent with only the forces of war and idiotic leaders affecting the military machine capabilities.
Sorry about the long winded entry