Do you mean at the strategic level skill or at the tactical level skill?
Strategically, I think the Red Army reached parity at Stalingrad. Stalingrad "Little Uranus" as big as it was only a small part of Big Uranus- the mega encirclement that Stavka planned of the entire Army Group South. In pursuit of this goal, Stavka not only encircled Stalingrad, but collapsed the Italian eight army- then sent balanced armored task forces deep into the German rear.
As perfectly strategically Blitzkreigish as Big Uranus was, the Soviets did not have the tactical skills to pull it off. German task forces, though outnumbered, systematically out fought and stopped their Soviet opposites. Even the main Soviet advance though the Italians began to falter as German battalions, regiments and divisions continued to outperform their Soviet opposites.
Soviet Strategic parity and German tactical advantage was again evident at the Kharkov counter offensive (highly skilled Soviet strategic planning was not matched at the tactical level). This led to a devastating German tactical counter attack that played on the tactical skills of Waffen divisions. Ditto for Kursk. The Germans were not beaten tactically, but stopped by Strategic insight.
In the end, I don't think the Soviets nor the western allies ever managed to match German tactical skills on a broad average (of course, individual exceptions exist)
Strategically I think both were at the absolute bottom in mid 1941. Germany for not preparing or planning into the winter of 1941/42 and the Soviets for relying on the Germans not attacking until the Soviets would be ready to attack themselves.
Tactically I don't think they were as far apart as we often image. If given the chance, and often without having a chance, a Red Army unit at tactical level (roughly squad-battalion level) would fight with extreme tenacity and often showing good use of terrain, firepower, movement etc.
The "Auftragstaktik/mission tactics" philosophy of the German army usually gave the German units the upper hand though, but usually at cost, as the "Reds" could be tough nuts to crack.
IMHO the huge difference came at the operational level - ie. the intermediate level between the front (tactics) and the overall allocation of resources and goals of the warfare (Strategy). This is the level where units capable of independent combat (from Brigade/Division and up) and deployed and lead into combat, and that includes TOEs and logistics. By 1940-41 the Wehrmacht was way ahead of any other army on the planet and in contrast the Red Army hardly had any operational level at all! The General officers had been shot, materiel dispersed to a degree where most units were critically short (de facto being static units) and the TOEs so extremely biased towards frontline strength that even the fully equipped units usually vapourised on the first combat contact. I guess this was a product of the Soviet system, where a career was made by reporting back to have fulfilled the quantitative goals in the plan. And here it was much easier to understand that a unit with 200 tanks in the inventory would be much better than one with 100 and in this context resources spent on mechanics and recovery vehicles could easily be seen as a waste of resources as would training the tank crews in locating the 100s of lubrication nipples and knowing which ones to used daily and which ones after 100 miles etc.
On top of that the overall tactical and operational doctrine was in chaos. Before WWII "deep operations" was the "way we fight" in the Red Army. Developed by Marshall Tuchachevsky and probably a much more deliberate take on "Blitzkrieg" than Blitzkrieg ever was, it had the Soviets produce more tanks in the 1930 than the rest of the planet combined. But then Tuchachevsky and his disciples were shot in the purges and the "doctrinal school" for a moment became more French inspired (ie. 1000 armoured units each of three tanks supporting the infantry rather than three units of 1000 tanks each supported by the infantry). Then came the German success in France 1940 and the pendulum swung back towards armour heavy manouvre units. This meant reinstitution of the Mechanised Corps - usually two armoured and a motorised Division - on paper the most powerful military units on the planet. To speed up the process most Rifle Divisions had to hand over most of their motor vehicles over to the Mechanised Corps and if anything was left it had to be shared with the numerous new units being formed in these years to achieve the goal of 500 Divisions by mid 1942.
The machine spitting out new units gave the SU an unmatched strategic perseverance when the army lost in 1941 had to be replaced, but the Soviets also had to realise that they at the operational level really couldn't handle units greater than a very simple Brigade.
IMHO this is the really critical time of the East Front. The Soviets won due to strategic perseverance and the Germans lost due to lack of the same - ie. the old stuff about not planning Barbarossa into 1942. With a foresighted planning, the Germans could have utilised their operational superiority to neutralise the Soviet perseverance into 1942. But they didn't - the operational superiority got blunted in the winter of 1941/42, and when it got temporarily sharpened again in mid 1942 and mid 1943 it was up against not only the Soviet perseverance but also against a Red army starting to get the grip of operations (and a Hitler replacing operational sense with a ditto neurosis).
NB: The lack of authoritative and sharp definitions of tactics/operations/strategy is remarkable, and the above definition is my own amateur version - so please don't blame any one else - but I think it is valuable to have this intermediate level "operation" - especially when discussing WWII.