Well, it's important to bear in mind that the USA was starting from a much higher starting point - especially when you consider the level of destruction brought on the USSR by WW2. The USSR's economy was always significantly smaller than the USA's - the closest it got was maybe 60% of the size (and bear in mind that the USSR had a 20-25% larger population, so in per capita terms the gap was even larger).

From the end of WW2 through to about 1970, both countries were going through booms. The Soviet growth rate was slightly faster. However, we should note that several US-aligned states, most notably Japan, were growing faster than either of them. From the 1970s onwards, both sides' growth rates weakened, but the Soviets slowed more.

I'd argue that the main period of fear in the US about the Soviet economy wasn't in the post-war years but in the 1930s. The US was still languishing in the Depression, while the Soviets were officially reporting annual GDP growth rates of more than 10% year after year. Most economists now believe that the official Soviet stats are exaggerated and the annual growth rates were probably never higher than 8-9%, but the official stats were readily believed by shocked and scared US officials, many of whom did indeed begin to fear that the Soviet system might be more efficient.

While a trace of this did remain after the war, it was never at the same scale - the US was going through perhaps its most prosperous period ever, which made the Soviet growth rate - which while still strong, was not at the same speed as the 1930s - much less noticeable.