All factors have been mentionned by different OPs, but I will present you a summary of how the Axis aviation went from victory to defeat:
Step one: get tactical defeats
The battle of Britain, the battle of Midway, are some examples of tactical defeats of the Axis aviation. They were lost against an opponent that was not threatened by an other mean (no ground or naval offensive possible), thus the fact that the Germans/Japanese lost more aircraft was a criteria of tactical and strategic defeat.
However, the losses were huge but not decisive for the timeframe of the war.
Step two: get points of attrition
The year 1942 was a year of attrition fight of all fronts, and this year leads to a turning point because of these battles. For the aviation, the fight on Malta, on Guadalcanal or Stalingrad were points of attrition were heavy losses on both sides allowed the capacity of production and training of the Allied states (and mainly USA and USSR) to express themselves.
In 1941, there was also some of these battles of attrition like in North and East Africa between the Italian and the British air forces.
Step three: loose the battle of bombings
During all these battles, the Axis air forces did not inflicted major destructions to strategic objectives because they lacked heavy bombers (as mentionned by another answer).
The British and Americans did not. And they stroke hevaily the Italian and German industries, leading them to fail in replacing many parts of their forces.
Add the specific lack of oil and oil with high octane degree for Axis forces in both Europe and Asia theaters, and the air forces are particulary leveled down by these bombings.
Note that Japan suffered mostly of the submarine war, because bombings on its territory started later.
Step four: Don't have a major technological upper-hand
Despite major advances in rocket motors, neither actor of WW2 had a real uper hand in technology. Some advantages were even in the Allied side with the building of four motor-bombers and the disposal of very good classic engines (like the British Merlin).
On other factors, as mentionned by other answers, the Americans and the British had medium armed fighters that were well adapted to their opponents, while the Axis hat to developed specific twin engined fighters to fight the heavy bombers.
Step five: be also beaten on other fields
The Axis might have work around these events with great naval and land victories. But it did not obtain these victories, partly because of its unhability to gain the air superiority, partly because on land and sea, the Allies were also good challengers.