One of my favorite lines from Vasitha's yoga "I am not, nor is there other, nor is there nonexistence."
In what ways does this parallel with Buddhist thought?
In what ways does it differ?
"I am not, nor is there other"
Ultimately, "I" in Buddhism is understood to be atman. When referring to the brahmanical understanding of atman, this refers to a permanent/eternal/unchanging essence under one's complete control, thus, something that is not essentially dukkha.
The Buddha taught anatta (not-self) going through all phenomena experienced in order to observe "This is not mine, this is not I, this is not myself" and thus relinquishing the illusion that atman (this underlying "true self") is within the range of experience, something to be grasped.
"or is there nonexistence."
I'm not familiar with the referred literature, but as far as "nonexistence" above has equivalent meaning to "nonexistence" in the suttas, here is what the Buddha says in the Kaccaayanagotto Sutta:
"The world in general, Kaccaayana, inclines to two views, to existence [Eternalism] or to non-existence [Annihilationism]. But for him who, with the highest wisdom, sees the uprising of the world as it really is, 'non-existence of the world' does not apply, and for him who, with highest wisdom, sees the passing away of the world as it really is, 'existence of the world' does not apply.
"The world in general, Kaccaayana, grasps after systems and is imprisoned by dogmas. But he does not go along with that system-grasping, that mental obstinacy and dogmatic bias, does not grasp at it, does not affirm: 'This is my self.' He knows without doubt or hesitation that whatever arises is merely dukkha that what passes away is merely dukkha and such knowledge is his own, not depending on anyone else. This, Kaccaayana, is what constitutes right view.
"'Everything exists,' this is one extreme [view]; 'nothing exists,' this is the other extreme. Avoiding both extremes the Tathaagata teaches a doctrine of the middle: Conditioned by ignorance are the formations... [as SN 12.10]... So there comes about the arising of this entire mass of suffering. But from the complete fading away and cessation of ignorance there comes the cessation of the formations, from the cessation of the formations comes the cessation of consciousness... So there comes about the complete cessation of this entire mass of suffering."