This may seem like a cheap answer, but Telltale makes good story-based games, and picking one just doesn't prove that point enough. Most of their big name titles are on both Android and iOS, but not all of them.
The Walking Dead, Minecraft: Story Mode, and Game of Thrones come to mind immediately as games that Telltale knocked out of the park, and their mobile versions are the same games, one-to-one, with better controls for touch screen. Often times, games that are one-to-one from a home device to mobile are clunky and feel like they're not made for a smartphone. Telltale makes sure that isn't the case with their ports.
If that wasn't enough to herald them as the best story-based games to play on mobile, then maybe the tradition of Telltale making the first episode of a completed series completely free to serve as a demo will convince a point-and-click adventurers to check out one of the many series they've got.