By what metric are we measuring "better off"? Economically? Happiness? I ask sincerely, because there's a lot of things the average person has had to worry about in the USA in daily life that the USSR took care of.

When asking "average" citizen, do you want the "mean" citizen, the "median" citizen, or the "modal" citizen? This matters! The "mean" income in the US in 2016 was 46,550, the "median" was 31,099.

Also worth considering the racial and gendered lenses of human experience. While it's tempting to say "Well, most Americans during the Cold War were white," answering with that sincerely and uncritically would serve to reinforce hegemonic norms of the American experience that exclude and frankly destroy one of the most important facets of the American experience: its variety. And this scrutiny should also be applied to the USSR side: while it's tempting to think of the USSR as made entirely of Russians, but in 1970 only 53% of Soviet citizens were ethnic Russians!