No centralized, planned economy has ever outperformed a free market, capitalist one. Ever.
You would be wrong. There are several examples of this happening. One case would be the War Communism period of the USSR. They had double digit growth rates that outperformed every other economy in the world. How else do you think a country which was known for most of its population being indentured serfs not so long ago came go to being the power that produced the most tanks in WWII even while it was being bombed in the process?
The WWII example is completely invalid from a military history perspective. See "Feeding the Bear" by Van Tuyll for an introduction.
Truly staggering amounts of military and industrial aid were provided to the USSR during the war. This was very carefully planned in close coordination with Soviet officials: the Soviets had good weapon designs in many basic categories, so a major concern was to support Soviet manufacturing of those weapons: this allowed the Soviets to shut down many peacetime production processes, and convert others over to weapons. Huge amounts of goods were shipped via the Arctic convoys, and directly from the USA to the Soviet Union on Soviet flag ships (the USSR and Japan had a treaty that permitted this, but only for "nonmilitary" goods). Any single Arctic convoy would be typically carrying a billion dollars (in today's money) worth of aid. Over 20k US citizens were sent to the Middle East to build a railroad from Iran to the Soviet Union allowing additional goods to be shipped to the Indian Ocean and then transported by rail to the Soviets (this was for military goods that could not be shipped directly: it allowed the extremely dangerous Arctic route to be avoided).
It is estimated that 90-95% of certain critical goods used by Soviet Industry in the war, such as ball bearings, were provided to the Soviet Union from imports. Ball bearings are used in every piece of rotating machinery, including many places in tanks, artillery, aircraft, not to mention the machine tools used to make these and the ammunition they use, plus a wide variety of other industrial processing and fabrication equipment. Huge amounts of machine tools were shipped as well, and since many of the Soviet factories had been designed by US engineers prior to the war, this equipment could be used directly: it was already familiar. It is also estimated that 90% of Soviet aviation fuel for high performance aircraft was processed using US made equipment and chemical additives.
It's worth noting that both Britain and Germany actually needed to import much of their ball bearing production (the Germans imported from Sweden). Standard machine tools can't easily produce round objects, so producing these in large numbers is hard, and while the British attempted to build new assembly lines to produce these, they had lots of problems and production was never sufficient. Ball bearings were such critical components that major air raids were attempted to attack German production.
In addition, hundreds of thousands of vehicles were shipped to the Soviet Union. The vast majority of these were non-combat vehicles: they played a critical role in the logistics required to support modern warfare, not to mention manufacturing logistics. See Martin van Creveld's book for a general introduction to the logistics issues of warfare: basically in modern war attrition of equipment and supplies is huge, yet at the same time a wide variety of parts, fuels, lubricants, and other chemicals is required. This in turn means a nation needs a solid train network to get equipment near the front, and huge numbers of trunks to get equipment from the train depots to the units (both are also required to get goods to factories for refining and assembling). The Soviets were under-equipped with trucks to begin with, and most of these were lost in the first few months. As another example, the Soviets only produced 92 locomotives between 1942 and 1945: they received 1,911 locomotives and 11,225 railcars as Lend-Lease imports.
As Soviet tank production barely got ahead of losses until the last year of the war, it is clear that the Soviets did not have the manufacturing reserve (facilities, manpower, steel production, machine tools, and so forth) to also create hundreds of thousands of additional vehicles.
Also, huge amounts of food and winter clothing were shipped to the Soviets. This was critical, because the most productive agricultural land in the Soviet Union was in German hands for much of the war. Further, production of both types of goods was labor intensive (and worse, a lot of the machinery that could otherwise be used to support farming had been taken for military use!), and the Soviets had a huge labor problem - they had such a huge labor problem that they were the only nation in the war to resort to using significant numbers of women in the military.
The majority of this stuff was produced in the USA and Britian, with a highly capitalist approach. See Arthur Herman's book for a detailed discussion of how that was done, which goes into detail about many largely unknown people who played critical roles, such as Danish immigrant William Knudsen (who gave up his job as CEO of General Motors to work for $1 a year organizing the US wartime production effort!).
During the Cold War, a lot of Soviet propaganda was produced to try to conceal the Soviet dependence on the West (North Korea has done similar stuff in recent decades). After the Cold War ended, this went away, and many former-Soviet sources have written about this topic. From a logistics and manufacturing perspective, it seems likely that - without Western aid - the Soviets would only have had about 10-20% of the forces they were actually able to deploy (tanks, artillery, aircraft), and their soldiers would have been hungry, under-clothed, and lacking in ammunition - which clearly would have been a huge disaster.
Not to mention that arguably the T-34 and KV-1 were among the most advanced tank designs in WWII when they went into active service (gun, armor, engine, suspension, etc).
These designs were good designs in many respects. At the same time, the evidence suggests that Soviet engineers were forced to produce them by being threatened with having themselves and their families sent to the gold mines - a death sentence. Note that the suspension of the T-34 was initially designed by an American. Many of the factory designs used to make these, in turn, came from US engineers hired to work in the Soviet Union before the war. Also, the Soviets benefited from the Kalkin Gol conflict with Japan pre-war: they were the only nation to have combat experience to test their designs in a modern setting (as opposed to WWI, already ancient history). The T-34 in particular went through massive revision as a result. Soviet participation in the Spanish Civil War helped as well (though primarily in terms of aircraft production).