Little Buddha and Kundun, Martin Scorsese's 1997 film about the childhood of the 14th Dalai Lama, dramatize the same underlying practice, a search party testing a child against a predecessor's possessions to confirm a reincarnation, within four years of each other, and the contrast between how each film handles it is instructive. Kundun is grounded in one specific, documented history: Tenzin Gyatso, found in 1937, enthroned, educated, and eventually driven into exile by the Chinese occupation of Tibet, all real events involving a real, still-living subject.
Little Buddha invents its central case. Jesse Conrad is a fictional Seattle boy, one of three candidate children under consideration rather than history's one confirmed reincarnation, and the film uses that invented, still-undecided search as a frame for something Kundun does not attempt: a full retelling of Siddhartha Gautama's own life and enlightenment, staged as an internal story told to explain the search's stakes to a skeptical American child and, through him, to a general audience with no prior exposure to the tradition at all.
The two approaches serve different purposes. Kundun asks to be trusted as history and answers to the historical record accordingly, including the political consequences that record carried for its own studio in China. Little Buddha asks to be trusted as an honest composite, openly fictional at the level of its plot while claiming accuracy at the level of ritual and doctrine, a claim its Tibetan Buddhist consultants were brought in specifically to hold it to.