So "privatness" or the form of ownership is not really that important, what really matters is management style and, far more importantly, macro-economic factors. What sets Russia and Western Europe apart is the banking infrastructure and skilled industrial labor - the latter had them because commercialism and industrialization in the West developed over a long period of time, a few hundred years. Russia did not have them because Russia remained mainly feudal society that lived off raw exploitation of human and natural resources with little or no investment, at least until 1862 when feudalism was officially abolished.
So as the Result, Russia found itself a bit backward by, say, few hundred years vis a vis the West and needed to catch up pronto, or face serious military threat. So what really set the Russia case apart form the West is that "capitalist" institutions that developed more or less "organically" in the West (by this I mean banking and credit institutions, social networks, skilled labor, self-management etc.) were mostly absent in Russia and had to be implemented by design and form above. That argument is explicitly proposed by Alexander Gerchenkron, but Trotsky argued along similar lines.
Private ownership is not a matter of semantics, and Trotsky would have been the last to argue that it is. The divorce between ownership and control in large corporations is only relative and temporary. Corporations are owned by individuals and institutions that ultimately demand a return on their inventment. While CEOs may exercise a great deal of latitude, the bottom line counts in the end. It is ultimately a question of profits, not style. This was not the case in the USSR. The Soviet bureaucracy was entrusted with delivering the goods to the people, not owners. They were thrown out because they could no longer do so in sufficient quantity or quality.