A big reason why the performance of the panzer divisions was so good in 1941 and consistently good until 43 had to do with this outstanding preparatory effort in which they discovered the correct synergistic mix and the correct training doctrine. This added even more to their pre-war lead in executing mobile war. After 1941, the general organizational form did not change drastically throughout the war, as it was flexible doctrine that worked well.
This is what I talk about when I say that the German military of '40 and '41 is "experienced". They have actual, real life, experience operating a million men at a time in foreign and hostile territory. Theory aside, figures aside, you will see in real life where the stresses and weaknesses are in your organization. You will see which of your men, NCOs and officers are capable, which aren't yet but can be retrained, and which are hopeless. You will find which of your figures were wrong and where are the weakpoints. These are the things you TRY to emulate in maneuvers but never really do adequately. You will be more effective even if you find no changes to make in your doctrines.
But mostly in '41 (and much of '42) they benefited from an unusually unprepared Soviet military. What saved the Soviets was a combination of 3 things; The depth of the country that needed to advance as the Germans, after some 400-500 miles, started to run into limitations in supply and then the progress was in fits and starts until it ground to a halt (similar to the Allies in France, the Soviets during Bagration, etc.). The second was not the size of the Soviet army, but the size of its reserves. There were already some 15-18 million men who had had military training and were still of fighting age. This was why they were able to put more units together so quickly. Germany did not have this depth of reserves, and as an industrial society, the older the male population the more likely a potential soldier was also a necessary worker. And finally, as time went on the Soviets were no longer inexperienced and incompetent. By the Stalingrad counter attacks they had been at war for a year and a half.
The W. allies took two-three years to rework their system to a competitive standard and according their own needs. By 44', the Germans didn't have a particular edge anymore in mobile forces against the west.
The irony is that the three reasons the Germans gave for their defeat aren't really good explanations:
The weather - this is a neutral factor. The weather affects both sides and at times that helps either one. Remember that at first the Germans welcomed the first frosts as it meant the mud hardened and they could finally move and supply again.
The greater size of the enemy - This was always the case and they knew about this going in. 3 million men invaded in Barbarossa, and quickly killed or captured 4.1 million Soviet soldiers, so by definition they were outnumbered from the start. And in the latter offensives the Soviet operations would be on fronts where there were under 2 Soviet troops for every German defending, but the Soviets had learned on attack to have 3-5 to 1 in the area of the attack (often as the result of maskirovka operations).
Hitler's meddling - Until the summer of '44 Hitler often took the advice of his generals, and also at times he was right when they were wrong. Many of the generals we consider brilliant also still thought in terms of quick and decisive engagements to defeat the enemy. They were the ones who felt it was important to capture Moscow and Leningrad where it was Hitler who focused on the south and the resources. In that case Hitler was probably in the right in that this was going to be a long and drawn out conflict and its resolution would be political and not military (the same way that the capture of Poland, Czechoslovakia and France was defeating them politically and not militarily capturing them).
The more I learn about the nitty gritty of the war the less impressive the Germans are as compared to the myths. They had some sharp uniforms and started off with some great doctrines, but by '43 they were believing their own hype a bit too much. The reason we often think what we do about the Germans vs. the Russians is that prior to the fall of the USSR most of our history comes from the German side, and most of that is from the German generals who fought the wars of '39-'43... they were the ones who survived.