Hoo boy, what's this thread about again?
Germany had by far and away the most advanced and future proofed air force in 1939/1940 bar none. It had one of the world's most modern fighters with the best performance in service, it had a strong and numerous bomber force equipped with modern up-to-date bomber types with good warloads and performance, some of these bombers were equipped with nav/bombing aids that took the rest of the world at least two years to incorporate into their bombers, thus making the Kampfgeschwader potentially the most accurate bombing force in the world, it had a large structure built around intelligence gathering and support, such as coastal and weather reconnaissance, tactical and strategic photographic reconnaissance elements, it had good, well trained pilots and ground crew. Its tactics were honed on the crucible of the Spanish Civil War, and it had sound military doctrine with concepts far beyond those being taught to other air forces around the world. Any air force attempting to match the Luftwaffe in this time period had better be good.
Materially, the only air force in Europe and most likely the world that could match the Luftwaffe in terms of modernity was the RAF, but even then, in many comparative aspects, the RAF falls short, especially tactically and strategically. Where the British have their strengths however, is Britain itself (and her friends, of course), and the Germans learned that the hard way.
Where the Luftwaffe falls short is follow-up. Its initial first strike campaigns and actions were groundbreaking, but sustaining it all proved virtually impossible for Germany. The Battle of Britain wrought enormous losses and took the best that the Luftwaffe had to offer and pushed it to breaking point. The Luftwaffe lost so much against Britain materially, tactically and strategically. It lost a vast number of aircraft and aircrew and its industries struggled to follow through with timely attrition replacements of equipment and personnel - Britain completely outproduced the German war machine to end the Battle of Britain with more fighters than it had begun the battle with. Not only had it replaced the fighters it had lost, but it had built even more on top of that number - the same could not be said for the Luftwaffe.
Even its subsequent night bombing campaign against Britain over the next year/s couldn't be sustained without suffering enormous losses. At the time it needed replacement for those prewar bombers, it dropped the ball. Its major strategic bomber and medium bomber replacement projects were far too ambitious and promised far more than what the industry could deliver - no follow through. The Luftwaffe soldiered on through WW2 with the outdated, quirky and underperforming by 1945 He 111 still at the frontline. Sure, there are jets, rockets and missiles and other advanced technologies, but if there's anything that Germany's defeat teaches us it's that the Germans didn't get the basics right. Training, what to do with intelligence, industry geared for war, long term strategies and tactics to sustain the war effort. The hardest part about being the best is not getting to become Number One, it's staying there.
Changes of tactics and strategy by the Allies proved that the Luftwaffe (and the Germans) were running out of ideas. The blitzkrieg tactics that worked so well in 1940 were eventually ground down through attrition and underestimation of the staying power of her enemies. This happened in North Africa and most notably in Russia. No follow through.
In hindsight its easy to map out what we think the Luftwaffe needed, but in 1939/1940 it couldn't have been more prepared for war, even though experts assure us it wasn't. It was far more capable of waging modern war than any other air force in the world in 1939/1940. This is the dilemma; how to fix the Luftwaffe is not a material matter, but a structural one. Germany needs to change before the Luftwaffe gets that follow through it so desperately needed post 1941.