Most American films were banned in the Soviet Union. The ones that were allowed were those that were perceived to have an anti-capitalist, anti-western message or at least that could be spun that way.

As far as I know, Soviet films were freely available in the United States, but unpopular just as foreign language films are in America today. Also, their association with the Soviet Union gave them an extra stigma. Nevertheless, the Soviet film Moscow Does Not Believe in Tears won an Oscar for best foreign language film in 1980.

The Soviet Union would generally only allow highly censored versions of American movies that tended to show American society in an unfavorable light. This included The Grapes of Wrath which portrayed poverty and the oppression of the American working class, and The Color Purple which portrayed racial prejudice in American society.

Ironically, airing The Grape of Wrath in the Soviet Union backfired a bit, as it portrayed that even the poorest Americans could at least afford one car. At the time of the movie's release, a family car was still an unattainable luxury for many in the USSR.