Like it or not Russia defeated the bulwark of the German war machine, there is no question they suffered the brunt of the German military force that would have easily overwhelmed other allied nations, even possibly the US. Russia did so using that inefficient system to allocate resources.
They did not do this by simply chucking their soldiers at the Germans with the threat of being shot by a Peoples Party Officer if they tried to run back, and often repeated myth of why Russia was able to halt and then pursue the Germans back to Berlin.
Also, any discussion of Russia during WW2 needs to include Simo Hayha ("White Death"), just because he's the most amazing sniper in the history of the world.
They actually never had arms parity - USA had over a 20:1 ratio of nukes in the 1960's. The problem is, the :1 is still enough to wreck all sorts of havoc. Also, massively more infantry.
Edit: Sorry, my numbers were wrong, misremebered. 1964: USA 2,416 USSR 375 [1]. So more like 8:1... later on the USSR closed the gap, but the USA had better strategic positions with bases in Taiwan, South Korea, Japan, and West Germany, and they cut off Cuba from the USSR after the Cuban Missile Crisis.
At some point, nuclear forces are pretty much a binary thing -- either you have enough to guarantee a second-strike countervalue capability, or you don't. China seems to believe it can do this mission with ~200 warheads, today.
Capitalism more efficiently allocates the labor of people than a command/communist economy. Thus, for the same population, a capitalist economy has more wealth -- it can spend this on better consumer goods AND better military hardware. The tokens themselves don't matter.
As well, the "western world" was much bigger and better resourced than the soviet bloc, and started from a much higher level of development.
It's amazing that the soviets were able to maintain some level of parity as long as they did (maybe to 1960-1965 in most military forces); for some things, playing catch-up was easier than initial development (nuclear tech, lots of other weapons, many consumer products), so it was easier to remain in a close second place than to potentially be the leader.