First it must be said that hedonism in the modern sense was not the core of Epicurism: Epicurus used the word ἡδονή (hêdonê, "pleasure") in a less obvious sense.
Epicureans strove after ataraxia, "unperturbedness" of the soul: a state of mind where neither pain nor pleasure affected the soul too much. This was the highest "pleasure".
Mild pain and mild pleasure were acceptable; but great pleasure was ill advised, because it would eventually end, and thus lead to longing for more, which constitutes pain. When we long for something, our heart aches.
Because moderate pleasure did not compromise ataraxia, casual sex and good food were allowed. But falling in love and unhealthy gluttony led to pain and were anathema.
The Stoics practised apatheia, "absence of feeling": a state of mind where the soul experiences no emotion at all. That was the only way in which the soul could be completely free. Any emotion would bind it to the body.
Life is a cart pulled by dogs; you, as a dog, have a choice between struggling against it, thereby causing yourself grief, or simply running along, going neither too fast nor too slowly
Any sexual escapade or other enjoyment compromised one's apatheia. In addition, even moderate pleasure could destabilize the soul, subjecting it to greater pleasure by consequence, which would ultimately end in pain. There are some similarities to Buddhism.