I want to commend Nate and recommend his post as probably the most concise, direct, and clear that I have seen. Of course I don't have the personal knowledge to validate or correct any errors, so those who read this thread in the future please feel free to elaborate. But for future reference and to avoid interminable rabbit trails, I will pin this post to the top of this subforum where it will be easily visible. Thanks Nate ! The original post in its original context is here.
Of the ancient Indian philosophies of Ājīvika, Ajñana, Buddhism, Chārvāka, Jainism, Mīmāṁsā, Nyāya, Samkhya, Vaisheshika, Vedanta, and Yoga, we'll find the closest companion to Epicureanism in Chārvāka. Early Buddhism is most closely related to the Indian school of Ajñana, from which Pyrrhonism developed, so, in general, I don't think that comparisons between Buddhism and Epicurean philosophy are helpful. They are dissimilar and historically unrelated.
In terms of physics, Epicureanism shares the atomism of Ājīvika and Vaisheshika (though, both traditions propose a deterministic physics) as well as the materialism of Chārvāka.
It uniquely shares the ethics of Chārvāka, whereas every other tradition devalues hedonism.
We find the most similarity between Epicurean epistemology and Chārvāka, which justifies the criterion of direct physical and mental perceptions, without inference, comparison, or speculation. It is most dissimilar from Ajñana, which rejects all criteria of knowledge, followed closely thereafter by Buddhism, which avoids making any certain claims.
Epicurean theology is comparatively unique. Epicurus would have been opposed to the atheism of Ājīvika, Chārvāka, Nyāya, and Vaisheshika, as well as the agnosticism of Ajñana and Buddhism, as well as the immanent dualism and mysticism of Samkhya and Yoga, and also the divine idealism of Mīmāṃsā and Vedanta. The Jain universe of multiple, physical deities (the Tirthankaras), is the closest ancient Indian theology that in any way resembles Epicureanism. There is not, to my knowledge, any significant historical link between the two at any point in time.
As far as ancient Indian philosophies go, early Buddhism overwhelmingly contradicts Epicurean philosophy. They are at the opposite ends of the epistemological spectrum, propose completely different goals in life, and are only barely physically compatible if, for no other reason than early Buddhism's refusal to provide any hard answers on physics.
Whereas Epicureanism is most similar to Chārvāka and, to an extent Ājīvika and Vaisheshika, Buddhism shares intellectual similarities with Ajñana and Prryhonian Skepticism, and the meditative practices with Vedanta and Yoga. Buddhism's propositions are much closer to Epicurus' opponents than to Epicurus in any meaningful way.