The Soviet Union was able to innovate in the areas they chose to sink resources into but innovation was clearly not as widespread as evidenced by their decades of stagnation from the 60s onwards.
They were still innovating in military technology in the 80s but analysis since their collapse analysis that they were at least 20% of GDP on defence, if not as high as 40%.
The West managed to match and surpass Soviet military and scientific advances without sacrificing consumer goods or the economic wellbeing of their people.
Innovation is a term inherently tied to products sold at markets in product cycles that change over time. I think you're looking for the term invention.
I'm not trying to downplay their accomplishments, but how much of their scientific advances from the 40s-60s were due to capturing ex-Nazi tech (and scientists) or stealing from the US via their incredible intelligence efforts?
I am very sure the west sacrificed a lot of wellbeing because of the vast amount of money spent on war. Peace time was great.