I asked a similar but more general question a few months ago with some good answers. Although none were specifically about the space race, you might find some of the answers from u/joshtothemaxx interesting.

https://www.reddit.com/r/AskHistorians/comments/56o4h9/how_powerful_were_soviet_computers_what/

Not talking space program directly, but about the right era and probably applies.

The newer and more revolutionary the section of the economy the greater the contrast between the United States and us. We have exceeded America in coal production but lag in extraction of oil, are ten times behind in natural gas and production of electric power, hopelessly behind in the chemical field, and immeasurably behind in computer technology. The last is especially essential, for the introduction of the computer into the economy is a factor of decisive importance, radically changing the character of the system of production and all culture. The phenomenon is justly called the second industrial revolution. Yet the capacity of our computers is hundreds of times less than that of the United States, and as regards utilizing computers in the economy the disparity is so great that it is impossible even to measure it. We simply live in a different epoch.

From a joint letter by Valentin Turchin, Andrei Sakharov, and Roy Medvedev to the leaders of the Soviet Union in 1970, reproduced in Turchin's book The Inertia of Fear and the Scientific Worldview. Turchin was a leading cybernetician and computer scientist and this passage is probably mostly his contribution.