It's reductive, but not totally inaccurate. The Stoics hated the Epicureans, because the Epicureans preached withdrawal from politics and the quest for political (military) honors, whereas the Stoics made those one of the defining principles of the virtuous life. Stoicism was adapted to imperialism in a way Epicureanism was not. Same way Pauline/proto-orthodox Christianity won out over the diversity of early Christianity --- it was usable by the Roman Empire.