In the roman empire, the west used latin and latin dialects as lingua franca, the eastern half used greek. It was the language of philosophy and the intellectuals, so there was no local lower-prestige language that could be replaced by latin. Latin was adopted in West Rome precisely because local languages were regarded as "lower class" and "lower prestige". So if you wanted to climb that social ladder, you better assimilate. In the East, greek already was the "higher class" language before Rome even set foot in greek city states. And the reverence Rome had to greek culture, history and language ensured that the Eastern empire stayed greek dominated.