In terms of equipment: mid-1942. In terms of skill... well, as others have noted that's more complicated. Gary Grigsby's War in the East has an interesting way of judging the troop quality of formations at the tactical-operational level. Obviously there are issues with taking video game mechanics face at value, particularly ones which are relatively abstracted as is the case here, but I find it can be useful as an illustrative example.
In any case, in War in the East what would be referred to as "tactical-operational skill" tends to be divided into two numerical values: morale and experience. "Morale" in this case refers not just too what we think of when people say the words morale, but also the realism and capability of the basic training that has been received and it's impact upon discipline and cohesion. Experience refers too both more advanced training (such as exercises and wargaming) as well as combat experience. The two influence each other, in that a counter's experience cannot be higher then it's morale.
Now, in addition to each counter's individual morale each nation in WitE also has a "national morale" that changes with time. In a sense, it's a "base morale" for regular counters: A counter which winds up below national morale will slowly climb up too what the national morale is. In addition to this, counters which are considered mechanized get a +10 bonus, although the Soviets only get this bonus starting in September 1942. Axis elite counters (namely SS and a number of other select formations) get a additional +5 bonus in 1941, a +10 bonus in 1942, and a +15 bonus from 1943 onwards. Soviet guards counter get another +10 bonus. These will stack, so a Soviet Guards Tank Corps from September 1942 onwards will have a base morale of the national morale+20. A counter which is ten or more over it's base morale will start to fall back down towards it's national morale. The impact of national morale on a formations Combat Value (which is the measures the game uses to determine who wins when combat occurs) is non-linear in that there are diminishing returns on increases/decreases, so a increase from 45 to 55 has a bigger impact then the increase from 55 to 65. The general rule of thumb is that, assuming full or near-full quantitative strength, a counter below 40 morale is useless, 40-50 morale can be used for defending, and 50+ is something fit for participating in an attack.
In terms of how national morale changes over time, that is hard coded and time-based: The Soviet national morale begins the game at 45 in 1941 and stays that way until August 1942, at which point it slowly starts to rise, reaching 50 by December 1942, 55 in June 1943, and maxes out at 60 in March 1944.
German national morale starts at 75 and slowly declines over the game before bottoming out at 55 at the start of 1945.
Axis minors national morale is 45 throughout the game, with the exception of Finland who are 75.
I wanna know, how was quality and quantity parity between the germans and soviets like at the eve of the Battle of Kursk, in July 1943?
To use the numerical value of national morale in War in the East, 56 for the Soviets and 67 for the Germans. Again, consider those numbers illustrative rather then descriptive.