It's because latin was the official language of the catholic church and church services were carried out in latin while the greek orthodox church used local languages.
Even before the Great Schism of 1054, Greek had been the language used to spread Christianity across southern and eastern Europe, i.e. across the Slavs. Even though the bible was always translated into a local language, Greek retained its prominence in the local education, hence the historical dominance (as opposed to Latin which didn't come into light until after the Renaissance and the spread of the scientific thought all over Europe).