This is a good question. Epicureanism is one of the most unique religions in the ancient world in that they were nearly atheistic. They believed that the gods were distant and did not care about the world. Hence, they argued that we should not fear the gods in any way. Also they actually developed a theory that the world was made of atoms! To the best of my knowledge, they were the first to develop atomic theory. Hence, they sought a rational explanation of how the world was created. One of the most famous Epicureans was the poet Lucretius. His epic work, On the Nature of Things lays out an epicurean framework.
Stoicism was very different. It was started in Athens by a man named Zeno and the basic idea behind Stoicism is that people should live in agreement with nature. In fact, according to Stoicism, virture is only possible when a person's will is in agreement with nature. Through determination, self-will, and unbiased thinking, they state that a person can live in accordance with universal reason, which they call "logos" in Greek.
Stoicism was the most popular religion among the upper-classes in the ancient world.