There was no common cause between Western countries and the USSR. The main cause of Western and, to a lesser extent, Japanese economic problems was high oil prices. The Soviet Union, meanwhile, should have benefited from high oil prices, but Soviet Type Economic Planning (STEP) was starting to falter in the 1970s. I say falter and not fail because the narrative around Soviet stagnation is often exaggerated, especially as it applies to the 1970s. During that decade, the Soviet Union was still catching up to the US economically, with its share of American GNP rising from 50% in 1965 to 60% in 1977. However, the Soviet model was starting to fail, as indicated by the only marginal gains it made on the US in spite of high oil prices.

The main cause of Western stagflation was high oil prices, triggered by two shocks - the 1973 Arab Oil Embargo and the Iranian Revolution. The Arab embargo, a response to perceived or actual support for Israel in the Yom Kippur War, initially targeting the US, Japan, UK, the Netherlands, and Canada. Despite its limited focus, it ended up trebling global oil prices within the span of half a year, owing both to the terms of the embargo (any country 'caught' re-exporting to an embargoed country would be punished) and the nature of the embargo; to ensure compliance, OAPEC mandated cuts in production and not just export restrictions. In 1979, a second shock came in the form of the Iranian Revolution, quickly followed by the Iran-Iraq War. During this war, Iran came under sanctions from several Western nations, and the Iranian air force almost totally destroyed the Iraqi oil industry by 1982. This second shock doubled oil prices again.

These 'price shocks' imposed a considerable cost on Western consumers and industry. The cost of all goods rose with the cost of transportation, and those whose productive processes involved petroleum such as fertilizer suffered the most.

Soviet stagnation was for entirely different reasons. To reiterate, the stagnation narrative as it applies to the USSR is an exaggeration, especially in the 1970s when the Soviets were still catching up to the West. That said, their failure to do so in a dramatic way in spite of the oil embargo owed to structural weaknesses in STEP. While successful for the first decades of its existence, Soviet Type Economic Planning started to fail in the 1970s owing to misaligned bureaucratic incentives and the failure of the 'material balancing' model of economic calculation.

According to Public Choice Theory, any bureaucracy mandated to provide its goods for free tries to ration its time and resources through other means. In plain terms - any bureaucracy that doesn't get paid commissions intentionally tries to make itself a massive pain to deal with, that way their 'clients' (be they the public or other officials) use them as little as possible. By the 1970s, noncompliance and noncooperation throughout the industrial machine was starting to become a serious problem for planners. The Soviet model required industries supply each other essentially for free, and promptly and accurately report. It never did these things without friction, but the increasing complexity of industry by the 1970s ensured that it was having a greater effect.

That said, 'informal rationing' likely did not harm Soviet competitiveness as much as the failure of material balancing. All employees who do not make commissions or goals-based performance bonuses tend to informally ration, including most employees in Western corporations; it was not a failure exclusive to the Soviet system. Far more particular to the USSR was its way of calculating inputs for economic plans. Refusing to base their plans around money owing to Marxist contempt for the ideal, Soviet central planners worked backwards from their output targets, determining targets for every stage of inputs, then calculating how many men and machines would be required to produce them. GOSPLAN, the central planning agency, did this all without the help of modern computers. As a natural consequence, hundreds of categories of less common goods were assigned an essentially random production quota as it was not efficient for the 'economic general staff' to calculate exactly how many 60° head angle, 1/8 PTF PVC grease fittings Volga Automotive Plant needed to fix returned chassis bearings on the Lada-1200S.

This problem, too, had a mitigating factor - planners could store excess supply in warehouses then decrease quotas for those goods. In practice, however, it was never that simple. Without budgets, Soviet businesses were input and not demand constrained. If Volga Automotive Plant receive 9,000 60 degree head angle grease fittings but only needed 7,000, its plant director was more likely to 'make use of' the extra 2,000 instead of sending them back. As with all entities with fixed allocations - they used them or lost them. This was not a necessarily counter-productive setup; the only way VAZ's director could make use of so much of a repair good was by putting out an announcement for Lada owners to come in for maintenance. Nevertheless, it resulted in the 'random' small quotas remaining in place, which led to growing pains as increasing economic complexity multiplied the number of small-quota goods.

A far bigger problem related to material balances was an anti-innovative bias in planning. Production estimates were based first and foremost on historical production, which meant new production methods were rarely prioritized. By the 1970s, the Soviet Union was falling behind in many categories of technological progression, most dramatically in techniques for steel production. This combined with the other problems associated with non-compensated behavior and material balancing to ensure the USSR failed to exploit the oil price hike and create an economic miracle.

Source:

Blinder, Alan. The Supply Shock Explanation of the Great Stagflation Revisited.

Lavoie, Dan. Rivalry and Central Planning.

Ellman, Michael. Socialist Planning, 3rd Ed.

Ofer, Gur. Soviet Economic Growth 1928-85.