Dear friends,
Although this question was directed to another, if I may, the Buddhist answer most generally is that "individuality is integral to the living being and is in EVERY way a temporary condition."
Buddhist ontology in the Mahayana traditions is radically different from Vaisnava ontology. It should be pointed out, however, that the philosophies of different schools make it very difficult to categorically state any position as being THE Buddhist position.
Even a question such as rebirth/reincarnation is not at all straightforward. Sutras and teachings can be found which lead one to believe that reincarnation is accepted, or that reincarnation is rejected, even within a single tradition. This tension is always present in Buddhism, and attempting to resolve it leads to some very subtle reasoning, or to enigmatic pronouncements which are difficult to interpret.
My experience has been that Buddhist laypersons from east Asia tend to accept reincarnation and the permanence of the unique individual but that Buddhist teachers, when pressed about the question, will either avoid answering directly, or deny the permanence of the unique individual.
Hare Krsna