I can answer your question partially, since I am only aware of tank production.

German tank production was ludicrously inefficient. Whenever requirements for a new design were composed, development would usually be given to several different companies, each of which was responsible for one component of the design, but naturally tried to grab as big of a piece of the pie as they could. This led to tank development and production being as much about politics as it was about engineering. It wasn't the best design that was put into service, it was the one that was backed by those who were best connected. This can be illustrated in the production of the Panzer III and Panzer IV tank. Even while production of the Panzer IV was going (by German metrics) very well and the Panzer III was still in early stages of small batch production, where the suspension design radically changed from series to series, but the 6th Waffenprüfamt was already petitioning to remove the Panzer IV from production and produce only the Panzer III, but with a different turret that could handle a 75 mm gun. This kind of internal bickering and inefficiency continued into WWII and plagued German tank design and production programs until the very end of the war.

Meanwhile, the USSR took the opposite approach. Even though there were still clashes between tank design bureaus, various directorates, contractors and subcontractors, everything changed when the Great Patriotic War broke out. The amount of organizations responsible for tank production was radically reduced when various factories that previously belonged to the People's Commissariats of Medium Machinebuilding, Heavy Machinebuilding, Ferrous Metals, Armament, etc. were reorganized under the umbrella of the People's Commissariat of Tank Production on 11 September 1941. Instead of a whole crowd of people's commissars and directors who could blame each other for production delays, there was now only one man with the responsibility and authority: Vyacheslav Malyshev. Stalin gave Malyshev one goal: make more tanks.

Luckily for Malyshev, the foundation for mass production was already laid before September. The T-34 was purposefully designed for mass production: the cast turret, composite hull, and special armour composition that did not require deficit raw materials were all developed before the German invasion. Substitute components using steel and iron instead of ferodo or aluminium were also developed and came in handy. Furthermore, each factory producing the T-34 was permitted to make their own changes to the design to tailor it to its individual capabilities, provided they did not break compatibility with the output of other factories. This is why there were so many different turret types: welded, stamped, cast, etc.

As far as light tanks, according to pre-war plans the Red Army's infantry support tank was going to be the T-50. This was a very advanced tank for its time, roughly on par with the German Panzer III medium tank, and even surpassing it in some ways. Unfortunately, this was also a very complicated and expensive tank. A number of factories nominally tasked with producing it had no equipment to deal with such a heavy product, plus it was also unclear where production of the engine could be ramped up, as every factory with the capacity to produce it was already building the V-2 engine to make T-34s.

The solution was production of the T-60 tank, which evolved from the T-40 amphibious reconnaissance tank. The result was not the greatest tank, but it was bulletproof and even resistant to light German artillery, worked well enough in an infantry support role, and used automotive components, meaning it could be produced in large numbers by automotive factories. By mid-1942 it was replaced with the T-70, also a very cheap and efficient tank, but with better armour and improved firepower. Even though the T-34 is the "canonical" Soviet tank of the WW2 era, the majority of Soviet tank production was made up of these light tanks in the early Great Patriotic War.

Malyshev also kept T-34 production and design focused on immediate needs. It was already clear by January 1940 that the T-34 was going to be replaced by the T-34M in 1941, but by the time the German invasion began only some components of the prototype were completed. Work to make a radically modernized T-34 never ended, but Malyshev kept most of his engineers focused on improving a tank that they already had, rather than retooling to produce a new one.

Interestingly enough, the summer of 1942 was when Malyshev lost his post of People's Commissar of Tank Production. On June 24th, he was replaced by Isaac Moiseyvich Zaltsman, formerly the director of the Kirov plant which produced KV tanks. One of the reasons why Malyshev was replaced was that he was not producing enough tanks, mainly T-34s. Zaltsman is often blamed by historians for trying to push through "his" KV over the "alien" T-34, but during his tenure as People's Commissar of Tank production the T-34 began to overtake other designs at Soviet factories, including Zaltsman's own Kirov factory. In addition to working on improving the amount of T-34s produced, Zaltsman had great impact on the quality of production and the efficiency of supply chains to tank factories. Zaltsman was even more focused on streamlining production, but not as forward thinking. His programs to produce a better tank than the T-34 stalled in early 1943. Despite Zaltsman's great achievements, Malyshev returned to the post of People's Commissar of Tank Production in 1943.

Sources:

http://www.tankarchives.ca/2017/01/pzkpfwiv-ausf-d-through-e.html

https://warspot.ru/3889-rozhdyonnyy-voynoy-kak-sozdavalsya-narkomat-tankovoy-promyshlennosti

https://warspot.ru/4621-pod-znakom-srednego-tanka

P. Samsonov Designing the T-34

R. Forczyk Tank Warfare on the Eastern Front 1941-1942 Schwerpunkt

R. Forczyk Tank Warfare on the Eastern Front 1943-1945 Red Steamroller

Y. Pasholok T-60 i mashini na yego baze