What are the differences in the fate of the Slavic peoples who converted to Catholicism and converted to Orthodoxy?
The Slavic peoples who adopted Orthodoxy in the cultural sense were close to Byzantium, while it existed, because it was in Constantinople that there was a patriarchy, in Moscow it appeared only in 1589. These peoples began to use the Cyrillic alphabet (Bulgarians, Serbs, Russians, Ukrainians, Belarusians, Macedonians, Montenegrins) and the Byzantine icon painting tradition. And even in the names it was reflected, Theodore instead of Theodore, etc.
Catholic peoples were closer to Rome, which influenced their ties with the Holy Roman Empire, counter-reformation and processes in Catholic Europe.
In Catholic Poland, for example, there was Magdeburg law, earlier than universities appeared in Russia (in the middle of the 14th century in Krakow and Prague, and here only in 1755).