Are you familiar with the Hindu concept of Atma? If so, what do you think are the differences between the atma and buddha nature?
@Terese I'm now in a little bit of a better state to give you a more complete answer, or so I feel. I don't think the Buddha would have 'fundamentally disagreed' with Shankara's Atman. He disagreed with the old Vedic understanding as far as I can see, because it made the ego eternal. Whereas there has been higher thought in Indian thinking from the beginning based on my knowledge of history- that the ego cannot be eternal because it can be deconstructed and attributed to sense states.
Buddhists early on like the Pugdalavadans (I already mentioned them) did think Buddhism might not be incompatible with a fine-tuned approach to a kind of 'Atman'.
Those Buddhists put forth alternate theories, as I've seen scholars of Indian philosophy call them. Ideas of a real self or real nature that is entirely unfathomable by the senses. The Pugdala was one such, which wasn't very different than Shankara's Atman- except the Pugdalavadans thought you were still only seeing a kind of shadow image when you could talk about the 'Atman' in any way. The Skandhas were distorting the real nature in order to grasp it, and this distorted perception is what the Pugdala is. Seeing the real self through the Skandhas, but the Pugdalavadans would say this only confirms a ground of being, and not anything further.
Citta in Mahayana is also described as one of these 'alternate theories'- when it means the essential heart.The crux of a Dharmic concept, and how it ties with the Buddha-nature, as an expression of it of sorts. There are other uses for Citta I don't know as much about.
I think the one area the Buddha may have possibly disagreed with the Atman of Advaita, is- don't Advaitists think the base sense of being a self is somehow tied in with the Atman, or am I mistaken? The Buddha would say we shouldn't go that far, and as I just mentioned- even the Pugdalavadans stopped short of it. At best, the Buddha might think we're going into dangerous territory there.
As far as I can tell though, the Buddha only taught Anatta because people were perpetuating the ego, and calling it a soul. This is possible to infer from the Buddha's explanation of 'Anatta' in the Samyutta Nikaya. He says that forms, perceptions, and so forth are 'not-self'- and this is all he means when he says Anatta. "Only this Radha: forms are not self, etc..."
Anatta doesn't necessarily mean there isn't a ground of reality.
As a Mahayanist I usually support this further with the Heart Sutra. This idea of a true/real nature of Dharmas. The Heart Sutra says:
"the characteristics of the voidness of all Dharmas is that they are not born and not destroyed, etc..."