Why were the tanks of the USSR so much better designed and so much more effective as opposed to their German counterparts?
I would argue there were two major reasons. The first was that Josef Stalin, as well as the Soviet High Command, did not interfere so heavily in Soviet weapon design and manufacture as opposed to Hitler. Hitler had a preoccupation with weapons that were formidable psychologically, and often ordered tanks as well as planes redesigned to achieve that purpose. The Tiger Tank was one such model (later redesigned, partially at Hitler's orders, into the "King Tiger). It was formidable, don't get me wrong, and had almost impenetrable armor and few external weaknesses with a powerful and accurate gun, but it was also plagued by mechanical problems and design delays and few of them were actually put into service. A great conversation piece, in other words, and something for soldiers to fear and share rumors about, but not a game changer as far as the war was concerned.
The Soviet T-34, by comparison, was a very simple, rugged, dependable and relatively light design that was mass produced much more effectively and in staggering numbers. The Americans overwhelmed the Germans with sheer numbers of Shermans, while the Soviets did the same with the T-34, which was also a much better tank.
The second major reason Soviet tanks were better involved the fact that their design reflected battlefield necessity and reality. They were built for the Russian cold because that was the environment they would be required to function in. It was built with sloping armor because it needed to compensate for German accuracy and firepower without compromising weight or speed. The result was a much more practical and effective tank that helped to turn the tide on the Eastern Front. It also didn't hurt that the USSR had nearly inexhaustible sources of oil and iron with which to construct and operate their tanks, again, unlike Germany.
Strategic Bombing of German industry, lack of raw materials, slave labor, no fuel, etc. - these were all factors in the design and manufacture of weapons of war.
Then there is another factor... The United States alone produced tanks in a ratio of 10-to-1 to Germany. American tanks were so bad that after Normandy the Army used to just put recruits out of basic training in them and send them off to die. Eventually we overwhelmed the Germans with numerical superiority.
On the Russian Front, the T-34, however, effectively made all German tanks produced to that date obsolete. In fact, at its height the T-34 was deemed so successful, and so capable in every role, that production of all other tanks except the IS-2 was stopped to allow all available resources to be used exclusively for this tank. The T-34 forced the Germans to adopt new, heavier designs such as the Panther and Tiger, which in turn forced upgrades to the Soviet, United States and British tank fleets. Perhaps more significantly to the ultimate course of the war, the move to more complex and expensive German tank designs overwhelmed the already critically strained German tank-production capability, reducing the numbers of tanks available to German forces and thus helping to force Germany to surrender the initiative in the war to the Allies.
Soviet tank production outstripped all other nations with the exception of the United States. The Soviets accomplished this through standardization on a few designs, generally forgoing minor qualitative improvements and changing designs only when upgrades would result in a major improvement.
Hitler ordered even heavier and stronger tanks to be produced, which led to the development of the heavy Tiger II, which replaced the Tiger I late in the war. Its powerful gun and very heavy armor made it superior to every Allied or Soviet tank in a head-to-head confrontation, but the underpowered engine and the enormous fuel consumption limited its use in maneuver warfare. Right before the end of the war there were plans for even more heavier tanks, such as the Panzer VIII Maus, but only small numbers, or in case of the Maus only prototypes, were produced.