The Stoics were continuum theorists, the Epicureans were atomists. These are conflicting positions. The Stoics upheld bivalence for propositions, the Epicureans seemed to be happy to give up bivalence for future contingents. These are likely to be conflicting positions. (I say likely, since the Epicureans did not subscribe to the Stoic theory of propositions or axiomata.) The Stoics were pantheists, the Epicureans were not. So they held conflicting positions. And so it goes on. (You find these distinctions in most introductions to Hellenistic philosophy, e.g. R.W. Sharples' "Stoics, Epicureans and sceptics: an introduction to Hellenistic philosophy".)
The Stoics and Epicureans were each other's main opponents during the Hellenistic period, since they were the strongest non-sceptical schools at the time. In late antiquity, both schools were badmouthed together, since both were materialists and thus their theories were incompatible with Platonist and Christian thought, which had by then become the dominant philosophical schools. For the same reason, most of their works were lost, since they were no longer copied and the existent papyri disintegrated.