True, but I am not swayed by the inefficiency argument. The big difference is the ability of the firm to externalize numerous costs: present in the market economies and absent in the state planned economies.
It has something to do with the firms' autonomy and pricing policy, which in the Soviet system was roughly based on the cost+ system; 'costmeaning the 'planned' cost of production, while '+' meaning various surcharges. It is easy to see that waste contributed to higher production costs which was then 'averaged' over the entire economy and paid by the buyers. Since both selling and buying units were state-owned, the state could not externalize those higher costs.
By contrast, autonomous firms in the market system can effectively externalize some of their cost (like unemployment, wasre disposal, or mismanagement) on the public sector, and thuse maintain the facade of efficiency i.e. high revenue/cost ratio through dischargning certain costs.
In other words, unlike under the central planning system, the price of the product does not include the full cost (including waste, social and environmental degradation, etc.) of its production -hence the illusion of greater efficiency.
In more general terms, American prosperity can be attributed to two factors: enormous profits made on 2WW, and the ability to discharge certain costs on someone else (either the public sector or third world countries). But on th eindividual firm level, I do not think there were any major differences in efficiency between the US and x-USSR, especially if efficiency is measured not by accounting gimmicks, but by the level of activities not related to the firm's goal like busy work, bureaucracy needed due to the lack of standardization, managerial schmoozing and kindred waste.