What is the most important distinction between Hindu and Buddhist teachings? From comparing Hindu and Buddhist texts, I have the impression that the most important difference is Atman v. anatta. Is this correct?
There is a deep correlation and similarity between the Buddha's teachings as represented by the Pali Canon (the Tripitaka) and modern Hinduism as represented by, for example, Patanjali's Yoga Sutras.
In highlighting differences between the two, one could say that the Buddha refused to talk about the nature of the self (the atman) or the nature/existence of the Absolute (God, in a monotheistic sense). The Buddha taught only about the universality of suffering and the means for ending that suffering (which involves the perfection of morality, concentration, wisdom and the opening of the heart).
'Anatta' is part of that teaching, called 'nonself.' For the Buddha, the universality of suffering is derived partially on the observation that nothing in life which we can touch (with the mind or body) can actually be said to be ours. And what is not 'ours' cannot be considered a part of 'ourself;' thus the teaching of anatta or 'nonself.' The Buddha asserted that any gods that could be interacted with were also included in that universality of suffering. Because of that assertion, Buddhists were seen as atheistic and a division between Buddhism and Hinduism was solidified on that ground.
However, when you look closer, you see that Hinduism has traditionally (from the Upanishads) accepted the Yoga that involves "neti, neti" or the observation that nothing that we can see is "atman" or "Brahman." Patanjali supports this in his Yoga Sutras by stating that the fundamental source of all ignorance is the false association between "drsyayoh" and "drastr," or "the Seen" and "the Seer" (Book 2.17) And ignorance is the basis for all the other kleshas or obstructions to Yoga. Seeing correctly that there is no real connection between the Seer and the Seen is fully compatible with the Buddha's teachings on anatta or 'nonself.'
Many Hindu practitioners in Vedic times considered "Brahma" to be the Absolute godhead. The Buddha taught that "Brahma" is a real "god" that, however, is not the same as the Absolute. In modern Hinduism, within Bhakti yoga, one can see any of a pantheon of 'gods' as the Absolute Godhead (as One without a Second). One then practices Yoga in order to achieve Union with the Absolute through the image and form of the individual god that one has chosen. Patanjali supports such a devotional yoga with the use of his phrase "Ishvara pranidhana" (Bk 1.23) This type of devotional yoga, however, does not free one from the other practices of yoga (ashtanga) such as the perfection of moralities and the eradication of ignorance about the relationship between the Seer and the See-able. Furthermore, Hinduism allows one to chose one's guru or preceptor as the representational form of the Absolute Godhead as one's focus within devotional yoga.
The apparent absence of support for such devotional types of yoga within the Buddha's teachings seem to indicate a difference with Hinduism. However, such devotion within Buddhism is accepted and supported if one chooses the Buddha, himself, as one's object of devotion and representation of the Absolute. So even this difference between Buddhism and Hinduism shrinks when examined closely.
So the most important differences are the theories explaining the SELF (atman) and the Absolute GOD. The Buddha avoids such theories as creating suffering and Hinduism includes them as helpful practices/contemplations. Outside of the theoretical differences, however, the similarities rather than the differences between the Buddha's teachings and modern Hinduism are more significant.