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One of the main goals of the Buddhist philosophy/religion is to be free of suffering.
Buddhism identifies ego, desire, non acceptance of impermanence, ignorance and all negative emotions(because the are self-destructive) as sources of suffering. In order to attain enlightenment the practitioner must know how all of these work and gain skill in self exploration, concentration and meditation.
How similar are these ideas of to what was taught by Epicureans and Stoics?
I'm no Stoic scholar but it seems to me...
As regards ethics they seem very similar up to a point. However, Stoicism has no 'enlightenment' and relies on speculation, and nor does it have a metaphysical foundation to justify and explain its ethics. (Thus in modern times even Materialists may call themselves Stoics despite the contradiction with the Stoic principle of Unity. It seems to be a metaphysical free-for-all.)
As an ethical practice Stoicism is not inimicable to Buddhism but their epistemology and ontology make them utterly different. They are bound to be when one is based on guesswork and the other on experience. Afaik Stoicism denies the possibility of knowing or understanding the Unity of the Universe and thus of properly explaining or justifying its ethical teachings.
It may be unfair, perhaps, but I would see modern Stoicism as an ethical scheme for those who do not believe the knowledge claims of the mystics but quite like their ethical teachings.