The difference between the Stalinist and post-Stalinist policies of Russification is that Stalin dealt a series of spectacularly violent blows to the Ukrainian nation, while his successors intiated a relatively nonviolent but relentless and systematic program of reducing the sphere of Ukrainian language and culture and raising the prestige of Russian language and culture.
For example, in spite of Stalin’s mass murder of Ukrainian intellectuals, Ukrainian-language education remained fairly intact. But under Khrushchev the Ukrainian language began to decline drastically from schools at every level, and this only intensified under Brezhnev. In 1948, the ratio of Ukrainian schools to Russian schools in Soviet Ukraine was 9.5:1. By 1987, over half of all pupils in Ukraine attended Russian-language schools. Moreover, Russian-language schools were much denser in the eastern and southern oblasts, which had been subjected to russification for a longer period, than in the western oblasts. In the big cities of the south and east, there were very few Ukrainian schools at all left by the end of the 1980s. There were no Ukrainian-language schools at all in Chernihiv, Donetsk, Luhansk, Simferopol, and Mykolaiv. Zaporizhzhia had one, Kharkiv two, Odesa three, Kirovohrad (now Kropyvnytskyy) four, and Kherson five. Only two spheres were left for Ukrainian-language education: village schools and schools in the three Galician oblasts (there were sixty-six Ukrainian schools in Lviv). The dominance of Russian-language education was, of course, a reversion to tsarist practice, and it is not suprising that the territories in which Soviet russificatory measures proved most successful were precisely those that had experienced tsarist rule the longest.
In Soviet Ukraine after Stalin, one of the most successful stratagems for promoting Russian-language education, a stratagem used by Khrushchev in his school reform of 1958-59, was to allow parents to choose between Russian-language or Ukrainian-language or minority-language schools for their children. Thus schools with the Russian language of instruction seem to have been freely chosen by parents who wanted to give their children a good start in life. But what appears as free choice is often enough not free at all when one considers the conditions under which a choice is made.
These conditions have been brilliantly analysed by Ivan Dzyuba in his book Internationalism or Russification? written in 1965 and soon about to be republished by Resistance Books. What Dzyuba demonstrated was that Soviet state policy systematically relegated the Ukrainian language and Ukrainian culture to a subordinate position, that it turned the latter into inferior, damaged goods in which many lost interest. Ukrainian-language periodicals and books were published in ever smaller quantities. In 1969 Ukrainian-language journals made up 46 percent of the journals published in Soviet Ukraine; by 1980 they only made up 19 percent. In 1959, 60 percent of books were in Ukrainian; by 1980 the percentage had dropped to 24. In the major universities of Ukraine, instruction was overwhelmingly in Russian, except for such subjects as Ukrainian literature and language. In the 1970s and 1980s, theater was largely performed in Russian. Ukrainian-language film was also curtailed. The Odesa film studio released sixty films from 1978 to 1988, only three of which were in Ukrainian. It seemed to many that the Ukrainian language and Ukrainian culture were being relegated to the ethnographic sphere, to the village. But even this was less than true, since the persecution of the church undid much of the binding of the traditional vernacular culture. One could be arrested for singing centuries-old Ukrainian Christmas carols!
Engaging in Ukrainian cultural activity put people at risk. That is why there were so many Ukrainian dissidents in the gulag in the 1970s and 1980s. Lenin in his day argued that the most dangerous form of nationalism in the Soviet polity was not any of the minority nationalisms, but Great-Power Russian chauvinism. However, even though in the course of Soviet history after Lenin’s passing, many thousands of Ukrainians were arrested and/or executed on suspicion of Ukrainian nationalism, no one was ever arrested for Russian chauvinism.
It is hardly any wonder that many citizens of Soviet Ukraine became Russophone. A Russian woman I knew in Leningrad back in the mid-1970s was surprised by my knowledge of Ukrainian. Why would I be interested, to quote her, in “such a narrow language”? But who was responsible for narrowing down the sphere of Ukrainian? The russifying Soviet state.
 These statistics come from Марія Ярмоленко, «Мовна політика в УРСР у 40-80-х роках XX століття», Наукові записки Інституту політичних і етнонаціональних досліджень ім. І.Ф. Кураса НАН України, вип. 3 (65) (2013): 372-75.