the Epicureans are the one who doesn´t accept Pain and try to avoid it.
Epicureans say Stoics doesn´t accept or want avoid (Painful/harmful) Emotions.
Epicureans seek pleasure, but at times they endure pain when it prevents a greater pain or leads to the pleasures that come with necessary things like food/shelter/health of the body and happiness of the soul -- This can be found in the Letter to Menoeceus.
I'm guessing that Stoics think that they need to be indifferent toward pleasures because they don't believe that there are certain pleasures which are easy to get, and also they don't trust that pleasure can lead to good results. And it seems that they may see pleasures as a distraction from being perfectly courageous (etc.) and a distraction from having the appearances in front of others of being virtuous. (Stoics want esteem in the eyes of others, but this won't necessarily lead to a happy life).
Emotions are a motivator for desiring, but if someone doesn't know how to prudently pursue pleasure, then they may think that they need to avoid feeling desire (and any emotions that lead to desire).