As i understand, "The dimension of nothingness" is an apex of equamity in as far as perception attainments go and "The dimension of neither perception nor non-perception" is an equanimity highest in as far as sustenance goes.
"There is the case, Ananda, where a monk, having practiced in this way — (thinking) 'It should not be, it should not occur to me; it will not be, it will not occur to me. What is, what has come to be, that I abandon' — obtains equanimity. He relishes that equanimity, welcomes it, remains fastened to it. As he relishes that equanimity, welcomes it, remains fastened to it, his consciousness is dependent on it, is sustained by it (clings to it). With clinging/sustenance, Ananda, a monk is not totally unbound."
"Being sustained, where is that monk sustained?"
"The dimension of neither perception nor non-perception."
"Then, indeed, being sustained, he is sustained by the supreme sustenance." Mn106