Why two stories? What do the two stories provide Pi Patel? What does the two-story structure provide Yann Martel as a writer?

Pi Patel told the first story to achieve distance between himself and his situation: drifting in a lifeboat in the Pacific Ocean for 227 days. In essence, to distance himself from reality.
Yann Martel used this structure to elevate the book from a simple story of survival to the story of Pi's spiritual journey. The first story describes Pi's journey using animals to represent the people on the lifeboat: a tiger, hyena, zebra, and orangutan. Pi's family had owned a zoo in Pondicherry, India, and Pi used the tools he learned there to train the tiger, and therefore to stay alive.
The second story is revealed only at the end, at which point the reader has completely accepted Pi's unusual situation. This story reveals the identity of the animals, most notably, Pi himself as the tiger.
If readers knew from the beginning who the animals represented, it would have been only a survival story. But Pi's journey was more than that, a fact repeatedly highlighted by flashbacks to his childhood religious studies and insistence on accepting multiple religions. With this structure, Martel could tell the story of Pi's spiritual journey, without the literal facts distracting the reader. The characters are boiled down into archetypal relationships, which also helped Pi distance himself from his situation so he could mentally survive the journey.

The first of the two stories in question is that of Piscine Molitor Patel (Pi), who survived for 227 days after the ship carrying him and his family, along with a collection of zoo animals, sank in the Pacific. When the ship sank, Pi ended up sharing a lifeboat with a hyena, a zebra, an orangutan, and a Bengal tiger. When Pi is rescued, the Japanese Ministry of Transport is skeptical and the officials investigating the shipwreck don't quite believe this first story. As a result, Pi tells them a second story, in which the animals are replaced by people. After having told the two stories, Pi asks the investigators:

So tell me, since it makes no factual difference to you and you can’t prove the question either way, which story do you prefer? Which is the better story, the story with animals or the story without animals?

The investigators end up choosing the story with animals and this, as the opening lines of the novel tell us, is the story that will make one "believe in God." One might take the device of the two stories as a strategy of the postmodern novel. One of the hallmarks of postmodernism is the subversion of traditional narrative. In offering two stories and asking the officials to pick one, Pi is also, in a way, engaging with the audience, who can pick one or the other of the stories; we don't have conclusive evidence in favor of either one. In this way, the story that offers a justification for God's existence becomes a choice and the novel can be read as espousing a fideistic approach to God's existence. The two stories also allow Martel to play with dichotomies such as reason/imagination, objectivity/subjectivity, materialism/idealism. The presence of these two stories allows Martel to explore these dichotomies from both sides.